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Constructing functions with prescribed pathwise quadratic variationNov 15 2015Apr 12 2016We construct rich vector spaces of continuous functions with prescribed curved or linear pathwise quadratic variations. We also construct a class of functions whose quadratic variation may depend in a local and nonlinear way on the function value. These ... More

An Exponential Cox-Ingersoll-Ross Process as Discounting FactorAug 30 2018We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spendings/dividend payments, given that the ... More

Utility maximization in Wiener-transformable marketsDec 29 2015We consider a utility maximization problem in a broad class of markets. Apart from traditional semimartingale markets, our class of markets includes processes with long memory, fractional Brownian motion and related processes, and, in general, Gaussian ... More

Small ball properties and representation resultsAug 28 2015We show that small ball estimates together with Holder continuity assumption allow to obtain new representation results in models with long memory. In order to apply these results, we establish small ball probability estimates for Gaussian processes whose ... More

Fractional Lévy processes as a result of compact interval integral transformationFeb 03 2010Aug 05 2010Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional L\'evy processes are defined by integrating the infinite ... More

Example of a Gaussian self-similar field with stationary rectangular increments that is not a fractional Brownian sheetMar 05 2014We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields with rectangular ... More

Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutionsDec 11 2011Nov 12 2012For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish an estimate ... More

Fractional Cox--Ingersoll--Ross process with non-zero <<mean>>Apr 05 2018In this paper we define the fractional Cox-Ingersoll-Ross process as $X_t:=Y_t^2\mathbf{1}_{\{t<\inf\{s>0:Y_s=0\}\}}$, where the process $Y=\{Y_t,t\ge0\}$ satisfies the SDE of the form $dY_t=\frac{1}{2}(\frac{k}{Y_t}-aY_t)dt+\frac{\sigma}{2}dB_t^H$, $\{B^H_t,t\ge0\}$ ... More

Option pricing in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. SimulationJan 06 2016We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation scheme is implemented. ... More

Pricing the European call option in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Exact formulasOct 07 2015We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of equivalent martingale ... More

Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck processApr 10 2016We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous ... More

Ruin probability in a risk model with a variable premium intensity and risky investmentsMar 27 2014We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential ... More

Random variables as pathwise integrals with respect to fractional Brownian motionNov 08 2011Sep 20 2012We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented ... More

Bounds and large deviation results for boundary non-crossing probabilities of Gaussian processesMar 14 2019We study boundary non-crossing probabilities $$ P_{f,u} := \mathrm{P}\big(\forall t\in \mathbb T\ X_t + f(t)\le u(t)\big) $$ for continuous centered Gaussian process $X$ indexed by arbitrary compact separable metrizable space $\mathbb T$. We obtain upper ... More

Existence and uniqueness theorems for solutions of McKean--Vlasov stochastic equationsMar 07 2016Jun 19 2016New weak and strong existence and weak and strong uniqueness results for multi-dimensional stochastic McKean--Vlasov equation are established under relaxed regularity conditions.

Optimization of small deviation for mixed fractional Brownian motion with trendJun 13 2018In this paper, we investigate two-sided bounds for the small ball probability of a mixed fractional Brownian motion with a general deterministic trend function, in terms of respective small ball probability of a mixed fractional Brownian motion without ... More

Asymptotic behavior of mixed power variations and statistical estimation in mixed modelsJan 06 2013Jun 19 2013We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter estimators ... More

Maximum likelihood drift estimation for Gaussian process with stationary incrementsDec 01 2016The paper deals with the regression model $X_t = \theta t + B_t$, $t\in[0, T ]$, where $B=\{B_t, t\geq 0\}$ is a centered Gaussian process with stationary increments. We study the estimation of the unknown parameter $\theta$ and establish the formula ... More

Stochastic viability and comparison theorems for mixed stochastic differential equationsNov 08 2012For a mixed stochastic differential equation containing both Wiener process and a H\"older continuous process with exponent $\gamma>1/2$, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise ... More

Replication of Wiener-transformable stochastic processes with application to financial markets with memoryAug 28 2018We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in general, Gaussian ... More

Consistency of the drift parameter estimator for the discretized fractional Ornstein-Uhlenbeck process with Hurst index $H\in(0,\frac12)$Jan 19 2015We consider Langevin equation involving fractional Brownian motion with Hurst index $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeck process and with unknown drift parameter $\theta$. We construct the estimator that is similar in form ... More

Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimationFeb 18 2016We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein-Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with probability 1 for ... More

New and refined bounds for expected maxima of fractional Brownian motionDec 23 2016Feb 05 2018For the fractional Brownian motion $B^H$ with the Hurst parameter value $H$ in (0,1/2), we derive new upper and lower bounds for the difference between the expectations of the maximum of $B^H$ over [0,1] and the maximum of $B^H$ over the discrete set ... More

Bounds for expected maxima of Gaussian processes and their discrete approximationsAug 01 2015The paper deals with the expected maxima of continuous Gaussian processes $X = (X_t)_{t\ge 0}$ that are H\"older continuous in $L_2$-norm and/or satisfy the opposite inequality for the $L_2$-norms of their increments. Examples of such processes include ... More

Stochastic representation and pathwise properties of fractional Cox-Ingersoll-Ross processAug 09 2017We consider the fractional Cox-Ingersoll-Ross process satisfying the stochastic differential equation (SDE) $dX_t = aX_t\,dt + \sigma \sqrt{X_t}\,dB^H_t$ driven by a fractional Brownian motion (fBm) with Hurst parameter exceeding $\frac{2}{3}$. The integral ... More

Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index $H> 1/2$Mar 03 2011We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

The rate of convergence of Euler approximations for solutions of stochastic differential equations driven by fractional Brownian motionMay 12 2007Feb 14 2008The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise ... More

Boundary Non-Crossings of Additive Wiener FieldsFeb 11 2014Jun 25 2014Let $W_i=\{W_i(t), t\in \mathbb{R}_+\}, i=1,2$ be two Wiener processes and $W_3=\{W_3(\mathbf{t}), \mathbf{t}\in \mathbb{R}_+^2\}$ be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower bounds for ... More

Construction of maximum likelihood estimator in the mixed fractional--fractional Brownian motion model with double long-range dependenceAug 12 2015We construct an estimator of the unknown drift parameter $\theta\in {\mathbb{R}}$ in the linear model \[X_t=\theta t+\sigma_1B^{H_1}(t)+\sigma_2B^{H_2}(t),\;t\in[0,T],\] where $B^{H_1}$ and $B^{H_2}$ are two independent fractional Brownian motions with ... More

Optimal stopping for Levy processes with polynomial rewardsJul 22 2015Explicit solution of an infinite horizon optimal stopping problem for a Levy processes with a polynomial reward function is given, in terms of the overall supremum of the process, when the solution of the problem is one-sided. The results are obtained ... More

An extension of the Lévy characterization to fractional Brownian motionNov 29 2006Mar 14 2011Assume that $X$ is a continuous square integrable process with zero mean, defined on some probability space $(\Omega,\mathrm {F},\mathrm {P})$. The classical characterization due to P. L\'{e}vy says that $X$ is a Brownian motion if and only if $X$ and ... More

On (signed) Takagi-Landsberg functions: $p^{\text{th}}$ variation, maximum, and modulus of continuityJun 14 2018Nov 25 2018We study a class $\mathfrak X^H$ of signed Takagi-Landsberg functions with Hurst parameter $H\in(0,1)$. We first show that the functions in $\mathfrak X^H$ admit a linear $p^{\text{th}}$ variation along the sequence of dyadic partitions of $[0,1]$, where ... More

Parameter estimation for Gaussian processes with application to the model with two independent fractional Brownian motionsAug 25 2018The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function, and $\theta$ ... More

On drift parameter estimation in models with fractional Brownian motionDec 11 2011We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard estimates and ... More

Convergence of solutions of mixed stochastic delay differential equations with applicationsJul 19 2014The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\gamma$-H\"older continuous process with $\gamma>1/2$ (e.g. a fractional Brownian motion with Hurst parameter greater than $1/2$). It is ... More

On the distribution of local times and integral functionals of a homogeneous diffusion processJun 06 2013In this article we study a homogeneous transient diffusion process $X$. We combine the theories of differential equations and of stochastic processes to obtain new results for homogeneous diffusion processes, generalizing the results of Salminen and Yor. ... More

Existence and uniqueness theorems for solutions of McKean--Vlasov stochastic equationsMar 07 2016Jul 26 2018New weak and strong existence and weak and strong uniqueness results for multi-dimensional stochastic McKean--Vlasov equations are established under relaxed regularity conditions. Weak existence is a variation of Krylov's weak existence for It\^o's SDEs ... More

Fractional calculus and path-wise integration for Volterra processes driven by Lévy and martingale noiseAug 30 2016We introduce a pathwise integration for Volterra processes driven by L\'evy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes, biology, and in environmental finance. Indeed they constitute a very ... More

Boundary non-crossing probabilities for fractional Brownian motion with trendSep 29 2013In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large trend function. ... More

Option pricing with fractional stochastic volatility and discontinuous payoff function of polynomial growthJul 25 2016We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a fractional Ornstein-Uhlenbeck ... More

Existence and uniqueness of mild solution to stochastic heat equation with white and fractional noisesMar 28 2018We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional $L^2(D)$-valued ... More

Asymptotic Properties of Drift Parameter Estimator Based on Discrete Observations of Stochastic Differential Equation Driven by Fractional Brownian MotionSep 25 2013We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic differential equations ... More

Approximation of fractional Brownian motion by martingalesMay 21 2012We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical ... More

Exact asymptotics of the uniform error of interpolation by multilinear splinesJan 13 2011The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design, finite element ... More

The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equationNov 29 2011We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of ... More

Rate of convergence of Euler approximations of solution to mixed stochastic differential equation involving Brownian motion and fractional Brownian motionNov 08 2011We consider a mixed stochastic differential equation involving both standard Brownian motion and fractional Brownian motion with Hurst parameter $H>1/2$. The mean-square rate of convergence of Euler approximations of solution to this equation is obtained. ... More

First-Order Modular Logic Programs and their Con:set servative ExtensionsAug 09 2016Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We also introduce ... More

Blow-up of solutions to a p-Laplace equationDec 16 2011Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field blows up in the L-infinity norm as the distance between the conductors tends to zero. We give here a concise rigorous ... More

First-Order Modular Logic Programs and their Conservative ExtensionsAug 09 2016Feb 17 2017Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We also introduce ... More

Solution Path Clustering with Adaptive Concave PenaltyApr 24 2014Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging ... More

Iterative Subsampling in Solution Path Clustering of Noisy Big DataDec 04 2014Jul 16 2015We develop an iterative subsampling approach to improve the computational efficiency of our previous work on solution path clustering (SPC). The SPC method achieves clustering by concave regularization on the pairwise distances between cluster centers. ... More

Central limit theorems in linear structural error-in-variables models with explanatory variables in the domain of attraction of the normal lawJun 06 2007Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these estimators, assuming ... More

Proceedings of Answer Set Programming and Other Computing Paradigms (ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, TurkeyDec 28 2013This volume contains the papers presented at the sixth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2013) held on August 25th, 2013 in Istanbul, co-located with the 29th International Conference on Logic Programming (ICLP 2013). ... More

SMT-based Constraint Answer Set Solver EZSMT+May 08 2019Constraint answer set programming integrates answer set programming with constraint processing. System EZSMT+ is a constraint answer set programming tool that utilizes satisfiability modulo theory solvers for search. Its theoretical foundation lies on ... More

Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary ReportAug 29 2011Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we ... More

The Effect of Slope in the Casimir Rack GearSep 17 2013The effect of slope for the rack gear in the massless scalar field model is considered. It appears, that the slope of profile surfaces can essentially change the value of normal Casimir force, whereas average value of tangential force remains almost unchanged. ... More

On the Shape Dependence of the Tangential Casimir ForceApr 19 2013The normal and tangential Casimir force for the rack gear is calculated numerically in the case of ideal boundary conditions for the electromagnetic field - perfect reflection on the boundaries. The resulting tangential force appears to be essentially ... More

Proceedings of Answer Set Programming and Other Computing Paradigms (ASPOCP 2012), 5th International Workshop, September 4, 2012, Budapest, HungaryJan 10 2013This volume contains the papers presented at the fifth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2012) held on September 4th, 2012 in Budapest, co-located with the 28th International Conference on Logic Programming (ICLP ... More

On the $L_p$-error of approximation of bivariate functions by harmonic splinesJan 14 2011Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). ... More

New multivariate central limit theorems in linear structural and functional error-in-variables modelsSep 06 2007This paper deals simultaneously with linear structural and functional error-in-variables models (SEIVM and FEIVM), revisiting in this context generalized and modified least squares estimators of the slope and intercept, and some methods of moments estimators ... More

Functional asymptotic confidence intervals for a common mean of independent random variablesJan 29 2009We consider independent random variables (r.v.'s) with a common mean $\mu$ that either satisfy Lindeberg's condition, or are symmetric around $\mu$. Present forms of existing functional central limit theorems (FCLT's) for Studentized partial sums of such ... More

Application of Malliavin calculus to exact and approximate option pricing under stochastic volatilityJul 31 2016The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density ... More

Asymptotic behavior of homogeneous additive functionals of the solutions of Itô stochastic differential equations with nonregular dependence on parameterJul 13 2016We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,d\xi_T(s)$, $t\ge0$, as $T\to\infty$. Here $\xi_T(t)$ is a strong solution of the stochastic differential equation $d\xi_T(t)=a_T(\xi_T(t))\,dt+dW_T(t)$, ... More

On the Malgrange isomonodromic deformations of non-resonant meromorphic (2x2)-connectionsDec 30 2011Feb 12 2012We study the tau-function and theta-divisor of an isomonodromic family of linear differential (2x2)-systems with non-resonant irregular singularities. In some particular case the estimates for pole orders of the coefficient matrices of the family are ... More

About hierarchy of multifrequency quasiperiodicity regimes in discrete low-dimensional Kuramoto modelFeb 25 2014Feb 26 2014A dynamics of a low-dimensional ensemble consisting of connected in a network five discrete phase oscillators is considered. A two-parameter synchronization picture which appears instead of the Arnold tongues with an increase of the system dimension is ... More

Detecting and monitoring foodborne illness outbreaks: Twitter communications and the 2015 U.S. Salmonella outbreak linked to imported cucumbersAug 24 2017This research uses Twitter, as a social media device, to track communications related to the 2015 U.S. foodborne illness outbreak linked to Salmonella in imported cucumbers from Mexico. The relevant Twitter data are analyzed in light of the timeline of ... More

On Transitive Systems of Subspaces in a Hilbert SpaceFeb 28 2006Apr 12 2006Methods of *-representations in Hilbert space are applied to study of systems of $n$ subspaces in a linear space. It is proved that the problem of description of $n$-transitive subspaces in a finite-dimensional linear space is *-wild for $n \geq 5$.

Noisy Supervision for Correcting Misaligned Cadaster Maps Without Perfect Ground Truth DataMar 12 2019In machine learning the best performance on a certain task is achieved by fully supervised methods when perfect ground truth labels are available. However, labels are often noisy, especially in remote sensing where manually curated public datasets are ... More

Coarse to fine non-rigid registration: a chain of scale-specific neural networks for multimodal image alignment with application to remote sensingFeb 27 2018We tackle here the problem of multimodal image non-rigid registration, which is of prime importance in remote sensing and medical imaging. The difficulties encountered by classical registration approaches include feature design and slow optimization by ... More

Disjunctive Answer Set Solvers via TemplatesOct 06 2015Answer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set solvers are ... More

Inequalities of Hardy-Littlewood-Polya type for functions of operators and their applicationsOct 05 2015In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function ... More

A Robust Preconditioner for High-Contrast ProblemsJan 04 2018A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained from a linear ... More

Kolmogorov problem on classes of absolute monotone and multiple monotone functions and its connection with Markov moment problemMar 23 2015In this paper we solve Kolmogorov problem about existence of a function with given norms of derivatives for classes of multiple monotone functions and absolute monotone functions in the case of arbitrary number of norms. We also show the connection of ... More

Another look at Bootstrapping the Student t-statisticSep 18 2012May 27 2013Let X, X_1,X_2,... be a sequence of i.i.d. random variables with mean $\mu=E X$. Let ${v_1^{(n)},...,v_n^{(n)}}_{n=1}^\infty$ be vectors of non-negative random variables (weights), independent of the data sequence ${X_1,...,X_n}_{n=1}^\infty$, and put ... More

Coupled systems with hyperchaos and quasiperiodicityApr 03 2015A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the parameter plane of ... More

Maps of several variables of finite total variation and Helly-type selection principlesJan 04 2010Given a map from a rectangle in the n-dimensional real Euclidean space into a metric semigroup, we introduce a concept of the total variation, which generalizes a similar concept due to T. H. Hildebrandt (1963) for real functions of two variables and ... More

Fages' Theorem and Answer Set ProgrammingMar 09 2000We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection with the emergence ... More

Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated SuspensionsAug 28 2006We present a two-dimensional (2D) mathematical model of a highly concentrated suspension or a thin film of the rigid inclusions in an incompressible Newtonian fluid. Our objectives are two-fold: (i) to obtain all singular terms in the asymptotics of the ... More

Preconditioned Iterative Methods for Diffusion Problems with High-Contrast InclusionsAug 02 2018This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the discrete system ... More

Simultaneous Approximation of a Multivariate Function and its Derivatives by Multilinear SplinesAug 24 2013In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation error on classes ... More

Kolmogorov's problem for completely and multiply monotone functions and the Markov moment problemSep 16 2015In this paper, we present the solution to Kolmogorov's problem for the classes of multiply monotone and completely monotone functions together with its connections to the Markov moment problem, Hermite-Birkhoff interpolation problem, and other extremal ... More

Incremental Learning for Semantic Segmentation of Large-Scale Remote Sensing DataOct 29 2018In spite of remarkable success of the convolutional neural networks on semantic segmentation, they suffer from catastrophic forgetting: a significant performance drop for the already learned classes when new classes are added on the data, having no annotations ... More

Finite speed of propagations of the electromagnetic field in nonlinear isotropic dispersive mediumsJan 22 2008May 15 2008We propose some modification of Maxwell's equations describing mediums which electric and magnetic properties are changed essentially after interaction with outer electromagnetic field. We show for such mediums that electromagnetic waves have finite speed ... More

Stechkin's problem for functions of a self-adjoint operator in a Hilbert space, Taikov-type inequalities and their applicationsMar 11 2017In this paper we solve the problem of approximating functionals $(\varphi(A)x, f)$ (where $\varphi(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another function $\psi (A)$ ... More

Kolmogorov's Problem on the Class of Multiply Monotone FunctionsAug 24 2013In this paper we give necessary and sufficient conditions for the system of positive numbers $ M_{k_1}, M_{k_2},..., M_{k_{d}},$ $0\leq k_1<...<k_{d} {\leq} r$, to guarantee the existence of an $r$-monotone function defined on the negative half-line $\RR_-$ ... More

Exact asymptotics of the optimal $L_{p,Ω}$-error of linear spline interpolationJan 14 2011In this paper we provide the exact asymptotics of the optimal weighted $L_p$-error, $0<p< \infty$, of linear spline interpolation of $C^2$ functions with positive Hessian. The full description of the behavior of the optimal error leads to the algorithm ... More

Recurrent Neural Networks to Enhance Satellite Image Classification MapsAug 11 2016The automatic pixelwise labeling of satellite images is of paramount importance in remote sensing. Convolutional neural networks represent a competitive means to learn the contextual features required to distinguish an object class from the rest. However, ... More

Learning Iterative Processes with Recurrent Neural Networks to Correct Satellite Image Classification MapsAug 11 2016Oct 26 2016While initially devised for image categorization, convolutional neural networks (CNNs) are being increasingly used for the pixelwise semantic labeling of images. However, the proper nature of the most common CNN architectures makes them good at recognizing ... More

Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximationNov 28 2013In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space $L_p$, $1\leqslant p\leqslant\infty$, of functions $f\in C^2\left([0,1]^2\right)$ with nonnegative Hessian by piecewise ... More

High-Resolution Semantic Labeling with Convolutional Neural NetworksNov 07 2016Convolutional neural networks (CNNs) have received increasing attention over the last few years. They were initially conceived for image categorization, i.e., the problem of assigning a semantic label to an entire input image. In this paper we address ... More

Representing First-Order Causal Theories by Logic ProgramsMar 23 2011Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the ... More

Optimal recovery of integral operators and its applicationsSep 15 2015In this paper we present the solution to the problem of recovering rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions ... More

Continuous-Time Markov Decisions based on Partial ExplorationJul 25 2018We provide a framework for speeding up algorithms for time-bounded reachability analysis of continuous-time Markov decision processes. The principle is to find a small, but almost equivalent subsystem of the original system and only analyse the subsystem. ... More

Reversible Digital Filters Total Parametric Sensitivity Optimization using Non-canonical Hypercomplex Number SystemsJan 25 2015Digital filter construction method, which is optimal by parametric sensitivity, based on using of non-canonical hypercomplex number systems is proposed and investigated. It is shown that the use of non-canonical hypercomplex number system with greater ... More

Progressive Tree-like Curvilinear Structure Reconstruction with Structured Ranking Learning and Graph AlgorithmDec 08 2016We propose a novel tree-like curvilinear structure reconstruction algorithm based on supervised learning and graph theory. In this work we analyze image patches to obtain the local major orientations and the rankings that correspond to the curvilinear ... More

Optimal Continuous Time Markov DecisionsJul 10 2015Jul 31 2015In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms have been proposed ... More

Recurrent Neural Networks to Correct Satellite Image Classification MapsAug 11 2016Apr 21 2017While initially devised for image categorization, convolutional neural networks (CNNs) are being increasingly used for the pixelwise semantic labeling of images. However, the proper nature of the most common CNN architectures makes them good at recognizing ... More

Goos-Hänchen effect for Brillouin light scattering by acoustic phononsMar 01 2019The lateral shift of an optical beam undergoing a Brillouin light scattering on acoustic wave in the total internal reflection geometry is studied theoretically. It is shown that the lateral shift depends on polarization (longitudinal or transversal) ... More

On one extremal property of a regular simplexJan 13 2011In this paper, we show that the $L_p$-error of asymmetric linear approximation of the quadratic function $Q({\mathbf x})=\sum_{j=1}^{d}x_j^2$ on simplices in $\RR^d$ of fixed volume is minimized on regular simplices.

The informal semantics of Answer Set Programming: A Tarskian perspectiveJan 26 2019In Knowledge Representation, it is crucial that knowledge engineers have a good understanding of the formal expressions that they write. What formal expressions state intuitively about the domain of discourse is studied in the theory of the informal semantics ... More