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Weak, Strong and Linear Convergence of a Double-Layer Fixed Point AlgorithmMar 28 2017In this article we consider a consistent convex feasibility problem in a real Hilbert space defined by a finite family of sets $C_i$. We are interested, in particular, in the case where for each $i$, $C_i=Fix (U_i)=\{z\in \mathcal H\mid p_i(z)=0\}$, $U_i\colon\mathcal ... More

Linear Convergence Rates for Extrapolated Fixed Point AlgorithmsMay 10 2018We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and cyclic cutter ... More

The Optimal Error Bound for the Method of Simultaneous ProjectionsApr 02 2017Sep 14 2017In this paper we find the optimal error bound (smallest possible estimate, independent of the starting point) for the linear convergence rate of the simultaneous projection method applied to closed linear subspaces in a real Hilbert space. We achieve ... More

Regular Sequences of Quasi-Nonexpansive Operators and Their ApplicationsOct 02 2017Feb 10 2018In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of the regularity ... More

Finitely Convergent Deterministic and Stochastic Methods for Solving Convex Feasibility ProblemsMay 14 2019We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation ... More

Convergence Properties of Dynamic String Averaging Projection Methods in the Presence of PerturbationsMar 22 2017Assuming that the absence of perturbations guarantees weak or strong convergence to a common fixed point, we study the behavior of perturbed products of an infinite family of nonexpansive operators. Our main result indicates that the convergence rate ... More

Weak, Strong and Linear Convergence of the CQ-Method Via the Regularity of Landweber OperatorsDec 18 2018We consider the split convex feasibility problem in a fixed point setting. Motivated by the well-known CQ-method of Byrne (2002), we define an abstract andweber transform which applies to more general operators than the metric projection. We call the ... More

An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean spaceApr 02 2013This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove ... More

Ultrametric Matrices and Representation TheoryMay 06 1997The consequences of replica-symmetry breaking on the structure of ultrametric matrices appearing in the theory of disordered systems is investigated with the help of representation theory, and the results are compared with those obtained by Temesvari, ... More

Charge Recombination in Undoped CupratesSep 08 2014Oct 31 2014We theoretically analyse the process of charge recombination in the planar Mott-Hubbard insulators with the aim to explain short picosecond-range lifetime of photoexcited carriers, experimentally studied via pump-probe experiments on the undoped cuprates. ... More

Dielectric breakdown in spin polarized Mott insulatorJan 18 2012Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin polarized insulator the ... More

Ultrafast charge recombination in photoexcited Mott-Hubbard insulatorNov 14 2012We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in picosecond ... More

Exact asymptotics of the current in boundary dissipated quantum chains in large external fieldsJan 10 2015Boundary driven quantum master equation for a general inhomogeneous (non-integrable) anisotropic Heisenberg spin $1/2$ chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong external field ... More

Order statistics and concentration of l_r norms for log-concave vectorsNov 30 2010We establish upper bounds for tails of order statistics of isotropic log-concave vectors and apply them to derive a concentration of l_r norms of such vectors.

Gaussian approximation of moments of sums of independent symmetric random variables with logarithmically concave tailsApr 03 2011We study how well moments of sums of independent symmetric random variables with logarithmically concave tails may be approximated by moments of Gaussian random variables.

Estimates of moments and tails of Gaussian chaosesMay 15 2005Feb 28 2007We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form $\sum a_{i_1,...,i_d}g_{i_1}... g_{i_d}$, where $g_i$ are i.i.d. ${\mathcal{N}}(0,1)$ r.v.'s. Estimates are exact up to constants depending on ... More

The GPU-based Parallel Ant Colony SystemMay 09 2016The Ant Colony System (ACS) is, next to Ant Colony Optimization (ACO) and the MAX-MIN Ant System (MMAS), one of the most efficient metaheuristic algorithms inspired by the behavior of ants. In this article we present three novel parallel versions of the ... More

On the moment event distance of Poisson processesJul 03 2015Mar 31 2016Consider the event distance between two i.i.d. Poisson processes with arrival rate $\lambda$ and respective arrival times $X_1,X_2,\dots$ and $Y_1,Y_2,\dots$ on a line. We give a closed analytical formula for the moment distance $\E{|X_{k+r}-Y_k|^a}, ... More

Flat manifolds with homogeneous holonomy representationMar 19 2018Oct 22 2018We show that a rational holonomy representation of any flat manifold except torus must have at least two non-equivalent irreducible subrepresentations. As an application we show that if a K\"ahler flat manifold is not a torus then its holonomy representation ... More

Asymptotics behaviour in one dimensional model of interacting particlesMay 04 2011We consider the equation u_t=\epsilon u_{xx}+(u\ K'*u)_x for x\in\mathbb{R}, t>0 and with \epsilon\geq 0, supplemented with a nonnegative, integrable initial datum. We present a class of interaction kernels K' such that the large time behaviour of solutions ... More

Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsionOct 05 2017We establish a link between the holomorphic derivatives of Thurston's hyperbolic gluing equations on an ideally triangulated finite volume hyperbolic 3-manifold and the cohomology of the sheaf of infinitesimal isometries. Moreover, we provide a geometric ... More

On Asymptotics of Moment Distance Between Sensors and Anchor PointsJun 22 2016Oct 28 2016The present paper contains additional asymptotic result over an earlier investigation of Kapelko and Kranakis. Consider $n$ mobile sensors placed independently at random with the uniform distribution on the unit interval $[0,1]$. Fix $a$ an odd natural ... More

Nonparametric deconvolution problem for dependent sequencesNov 26 2007Aug 13 2008We consider the nonparametric estimation of the density function of weakly and strongly dependent processes with noisy observations. We show that in the ordinary smooth case the optimal bandwidth choice can be influenced by long range dependence, as opposite ... More

Extremal particles in branching processessJun 06 2016Jun 07 2018The purpose of this study is to investigate two related spatial branching models with the unbounded branching intensity. The objective is to describe the asymptotic behaviour of the extremal particle.

Maximal inequalities for centered norms of sums of independent random vectorsJan 04 2015Let $X_1,X_2,\ldots,X_n$ be independent random variables and $S_k=\sum_{i=1}^k X_i$. We show that for any constants $a_k$, \[ \Pr(\max_{1\leq k\leq n}||S_{k}|-a_{k}|>11t)\leq 30 \max_{1\leq k\leq n}\Pr(||S_{k}|-a_{k}|>t). \] We also discuss similar inequalities ... More

Two-sided moment estimates for a class of nonnegative chaosesJun 06 2016We derive two-sided bounds for moments of random multilinear forms (random chaoses) with nonnegative coeficients generated by independent nonnegative random variables $X_i$ which satisfy the following condition on the growth of moments: $\lv X_i \rv_{2p} ... More

Irreducible euclidean representations of Fibonacci groupsJul 31 2015We show that every Hantzsche-Wendt group is an epimorphic image of a certain Fibonacci group.

Bahadur--Kiefer theory for sample quantiles of weakly dependent linear processesMay 10 2006Nov 28 2007In this paper, we establish the Bahadur--Kiefer representation for sample quantiles for a class of weakly dependent linear processes. The rate of approximation is the same as for i.i.d. sequences and is thus optimal.

Threshold phenomena for interference with randomly placed sensorsNov 19 2016Assume $n$ sensors are initially placed on the half-infinite interval $[0,\infty)$ according to Poisson process with arrival rate $n.$ Let $s \ge 0$ be a given real number. We are allowed to move the sensors on the line, so as that no two sensors are ... More

Seven dimensional flat manifolds with cyclic holonomyJan 13 2011Oct 19 2011We classify (up to affine equivalence) all 7-dimensional flat manifolds with a cyclic holonomy group.

Convergence acceleration of alternating seriesFeb 23 2017Apr 29 2018We propose a new simple convergence acceleration method for wide range class of convergent alternating series. It has some common features with Smith's and Ford's modification of Levin's and Weniger's sequence transformations, but its computational and ... More

Double parton scattering with high cross sectionsMar 13 2017The calculations of the double parton scattering cross sections are discussed. It is shown that the commonly used factorised formula is valid only in the limit of low cross sections. The applicability of this approximation is studied with a more general ... More

On the convergence acceleration of some continued fractionsAug 16 2011Mar 04 2012A well known method for convergence acceleration of continued fraction $\K(a_n/b_n)$ is to use the modified approximants $S_n(\omega_n)$ in place of the classical approximants $S_n(0)$, where $\omega_n$ are close to tails $f^{(n)}$ of continued fraction. ... More

Modified Paouris inequalityDec 09 2013The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l_r-norms and suprema of norms of coordinate ... More

On ${\cal Z}_p$-norms of random vectorsNov 06 2017To any $n$-dimensional random vector $X$ we may associate its $L_p$-centroid body ${\cal Z}_p(X)$ and the corresponding norm. We formulate a conjecture concerning the bound on the ${\cal Z}_p(X)$-norm of $X$ and show that it holds under some additional ... More

Tail and moment estimates for a class of random chaoses of order twoAug 19 2017Jun 07 2018We derive two-sided bounds for moments and tails of random quadratic forms (random chaoses of order $2$), generated by independent symmetric random variables such that $\lVert X \rVert_{2p} \leq \alpha \lVert X \rVert_p$ for any $p\geq 1$ and some $\alpha\geq ... More

Weak and strong moments of random vectorsDec 13 2010We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.

$L_1$-norm of combinations of products of independent random variablesMay 19 2013We show that $L_1$-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. nonnegative mean one random variables is comparable to $l_1$-norm of coefficients.

On some inequalities for Gaussian measuresApr 22 2003We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.

Truncated Variation, Upward Truncated Variation and Downward Truncated Variation of Brownian Motion with Drift - their Characteristics and ApplicationsDec 23 2009Dec 08 2011In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + \mu t, t\geq 0,$ where $(B_t)$ is a standard Brownian ... More

On Asymptotics of Moment Distance Between Sensors and Anchor PointsJun 22 2016The present paper contains additional asymptotic result over an earlier investigation of Kapelko and Kranakis. Consider $n$ mobile sensors placed independently at random with the uniform distribution on the unit interval $[0,1]$. Fix $a$ an odd natural ... More

Extremal particles in branching processessJun 06 2016The purpose of this study is to investigate two related spatial branching models with the unbounded branching intensity. The objective is to describe the asymptotic behaviour of the extremal particle.

Stability of solutions to aggregation equation in bounded domainsApr 24 2012Mar 19 2013We consider the aggregation equation $u_t= \div(\nabla u-u\nabla \K(u))$ in a bounded domain $\Omega\subset \R^d$ with supplemented the Neumann boundary condition and with a nonnegative, integrable initial datum. Here, $\K=\K(u)$ is an integral operator. ... More

Moments of unconditional logarithmically concave vectorsApr 03 2011We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.

On Weak Tail Domination of Random VectorsNov 09 2007Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular weak tail domination implies strong tail domination. In particular positive ... More

Exciton Recombination in One-Dimensional Organic Mott InsulatorsAug 14 2015We present a theory for the recombination of (charged) holons and doublons in one-dimensional organic Mott insulators, which is responsible for the decay of a photoexcited metallic state. Due to the charge-spin separation, the dominant mechanism for recombination ... More

Outer Approximation Methods for Solving Variational Inequalities in Hilbert SpaceFeb 02 2017In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $C$. We assume that the set $C$ can be outerly approximated by the fixed ... More

Hanson-Wright inequality in Banach spacesNov 01 2018We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds up to additional logarithmic factors. Moreover in a certain class of Banach ... More

A Survey on Spatial Co-location Patterns Discovery from Spatial DatasetsFeb 06 2014Spatial data mining or Knowledge discovery in spatial database is the extraction of implicit knowledge, spatial relations and spatial patterns that are not explicitly stored in databases. Co-location patterns discovery is the process of finding the subsets ... More

Properties of strongly dipolar Bose gases beyond the Born approximationNov 22 2016Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections ... More

Route to chaos in generalized logistic mapFeb 01 2015Motivated by a possibility to optimize modelling of the population evolution we postulate a generalization of the well-know logistic map. Generalized difference equation reads: \begin{equation} x_{n+1}=rx^p_n(1-x^q_n), \end{equation} $x\in[0,1],\;(p,q)>0,\;n=0,1,2,...$, ... More

Weakly symmetric biserial algebrasFeb 13 2018We introduce the class of generalized biserial quiver algebras and prove that they provide a complete classification of all weakly symmetric biserial algebras over an algebraically closed field.

On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg FunctionsOct 15 2012May 16 2013For a real c\`{a}dl\`{a}g function f and a positive constant c we find another c\`{a}dl\`{a}g function, which has the smallest total variation pos- sible among all functions uniformly approximating f with accuracy c/2. The solution is expressed with the ... More

Wavelet regression in random design with heteroscedastic dependent errorsSep 02 2009We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales, $f\in\mathcal{B}^s_{\pi,r}$, ... More

A note on suprema of canonical processes based on random variables with regular momentsJun 25 2014We derive two-sided bounds for expected values of suprema of canonical processes based on random variables with moments growing regularly. We also discuss a Sudakov-type minoration principle for canonical processes.

Integration with respect to model-free price paths with jumpsNov 25 2015Sep 09 2016For every adapted, c\`agl\`ad process (strategy) $G$ and typical c\`adl\`ag price paths whose jumps satisfy some mild growth condition we define integral $G\cdot S$ as a limit of simple integrals.

Quadratic variation of càdlàg semimartingales as a.s. limit of the normalized truncated variationsAug 02 2017Jan 08 2019For a real c\`adl\`ag path $x$ we define sequence of semi-explicit quantities, which do not depend on any partitions and such that whenever $x$ is a path of a c\`adl\`ag semimartingale then these quantities tend a.s. to the continuous part of the quadratic ... More

Time-dependent generalized Gibbs ensembles in open quantum systemsJan 23 2018Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class ... More

Activating many-body localization in solids by driving with lightJun 12 2018Due to the presence of phonons, many body localization (MBL) does not occur in disordered solids, even if disorder is strong. Local conservation laws characterizing an underlying MBL phase decay due to the coupling to phonons. Here we show that this decay ... More

Integrable solutions of inhomogeneous refinement type equations on intervalsJul 27 2015Given a probability measure $P$ on a $\sigma$-algebra of subsets of a set $\Omega$, an interval $I\subset\mathbb R$, $g\in L^1(I)$, and a function $\varphi\colon I\times\Omega\to I$ fulfilling some conditions we obtain results on the existence of solutions ... More

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequencesSep 26 2007Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results ... More

Inequalities between ground-state energies of Heisenberg modelsOct 20 2014The Lieb-Schupp inequality is the inequality between ground state en- ergies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb-Schupp inequality has been tested for spin systems ... More

Holonomy groups of flat manifolds with $R_\infty$ propertyApr 29 2011Sep 11 2013Let $M$ be a flat manifold. We say that $M$ has $R_\infty$ property if the Reidemeister number $R(f) = \infty$ for every homeomorphism $f \colon M \to M.$ In this paper, we investigate a relation between the holonomy representation $\rho$ of a flat manifold ... More

Between Sobolev and PoincaréMar 07 2000We establish a family of functional inequalities interpolating between the classical logarithmic Sobolev and Poincar\'e inequalities. We prove that they imply the concentration of measure phenomenon intermediate between Gaussian and exponential. Our bounds ... More

Approximations of Bond and Swaption Prices in a Black-Karasiński ModelJun 01 2015We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasi\'{n}ski interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Lo\`{e}ve expansion. Formulas are easily computable and ... More

Equivariant Cartan-Eilenberg supergerbes II. Equivariance in the super-Minkowskian settingMay 13 2019May 22 2019This is a continuation of a programme, initiated in Part I [arXiv:1706.05682], of geometrisation, compatible with the SUSY present, of the Green-Schwarz $(p+2)$-cocycles coupling to the topological charges carried by $p$-branes on reductive homogeneous ... More

Decay of Dirac Massive Hair in the Background of Spherical Black HoleMay 06 2008The intermediate and late-time behaviour of massive Dirac hair in the static spherically symmetric black hole spacetime was studied. It was revealed that the intermediate asymptotic pattern of decay of massive Dirac spinor hair is dependent on the mass ... More

Linearity of regression for weak records, revisitedNov 01 2015Jul 11 2016Since many years characterization of distribution by linearity of regression of non-adjacent weak records E(W_{i+s}|W_i) = \beta_1 W_i+\beta_0 for discrete observations has been known to be a difficult question. Lopez- Blazquez (2004) proposed an interesting ... More

On pathwise uniform approximation of processes with càdlàg trajectories by processes with finite total variationJun 14 2011Jun 29 2012For any real-valued stochastic process X with c\`adl\`ag paths we define non-empty family of processes, which have finite total variation, have jumps of the same order as the process X and uniformly approximate its paths: This allows to decompose any ... More

Necessary and Sufficient Conditions for the Strong Law of Large Numbers for U-statisticsJan 17 1999Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an analogous form.

Equivariant Cartan-Eilenberg supergerbes II. Equivariance in the super-Minkowskian settingMay 13 2019This is a continuation of a programme, initiated in Part I [arXiv:1706.05682], of geometrisation, compatible with the SUSY present, of the Green-Schwarz $(p+2)$-cocycles coupling to the topological charges carried by $p$-branes on reductive homogeneous ... More

Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tailsAug 30 2015We derive two-sided estimates for random multilinear forms (random chaoses) generated by independent symmetric random variables with logarithmically concave tails. Estimates are exact up to multiplicative constants depending only on the order of chaos. ... More

Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tailsJul 08 2010We present two-sided estimates of moments and tails of polynomial chaoses of order at most three generated by independent symmetric random variables with log-concave tails as well as for chaoses of arbitrary order generated by independent symmetric exponential ... More

Constructions of contact forms on products and piecewise fibered manifoldsApr 07 2012Aug 11 2013We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This result is extended ... More

On tails of exit times of multidimensional Lévy processesSep 17 2018Nov 06 2018Using a very simple argument based on the indepenence of increments and the fact that in a finite dimensional space $R^{d}$ there are not too many directions, we derive a theorem stating that exit time of any (non-constant) L\'{e}vy process on $R^{d}$ ... More

Properties of strongly dipolar Bose gases beyond the Born approximationNov 22 2016Mar 24 2017Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections ... More

Two-sided estimates for order statistics of log-concave random vectorsJan 06 2019We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants in the unconditional ... More

The LIL for canonical $U$-statisticsApr 11 2006Jun 13 2008We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical $U$-statistics of arbitrary order $d$, extending the previously known results for $d=2$. The nasc's are expressed as growth conditions on a parameterized ... More

On a generalisation of the Banach indicatrix theoremMar 05 2015Sep 12 2016We prove that for any regulated function $f:\left[a,b\right]\rightarrow\mathbb{R}$ and $c\geq 0$ the infimum of the total variations of functions approximating $f$ with accuracy $c/2$ is equal $\int_{\mathbb{R}} n_{c}^{y} \mathrm{d} y,$ where $n_{c}^{y}$ ... More

Comparison of weak and strong moments for vectors with independent coordinatesDec 07 2016We show that for $p\ge 1$, the $p$-th moment of suprema of linear combinations of independent centered random variables are comparable with the sum of the first moment and the weak $p$-th moment provided that $2q$-th and $q$-th integral moments of these ... More

Weak and strong moments of l_r-norms of log-concave vectorsJan 07 2015Nov 02 2015We show that for $p\geq 1$ and $r\geq 1$ the $p$-th moment of the $l_r$-norm of a log-concave random vector is comparable to the sum of the first moment and the weak $p$-th moment up to a constant proportional to $r$. This extends the previous result ... More

CLT for supercritical branching processes with heavy-tailed branching lawMar 14 2018Mar 21 2018Consider a branching system with particles moving according to an Ornstein-Uhlenbeck process with drift $\mu>0$ and branching according to a law in the domain of attraction of the $(1+\beta)$-stable distribution. The mean of the branching law is strictly ... More

Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility processAug 16 2011We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which tends to infinity). ... More

Inhomogeneous refinement equations with random affine mapsJun 24 2015Given a probability space $(\Omega,{\mathcal A},P)$, random variables $L,M\colon\Omega\to\mathbb R$ and $g\in L^1(\mathbb R)$ we obtain two characterizations of these $f\in L^1(\mathbb R)$ which are solutions of the inhomogeneous refinement equation with ... More

Asymptotics of the truncated variation of model-free price paths and semimartingales with jumpsAug 06 2015Feb 15 2016We prove that typical (in the model-free finance setting) price paths with jumps may be uniformly approximated with accuracy $c>0$ by paths whose total variation is of order $1/c.$ A more precise result is obtained for semimartingales with jumps.

Asymptotics of the truncated variation of model-free price paths and semimartingales with jumpsAug 06 2015Jun 23 2017We prove that typical (in the model-free finance setting) price paths with jumps may be uniformly approximated with accuracy $c>0$ by paths whose total variation is of order $1/c.$ A more precise result is obtained for semimartingales with jumps.

On the boundedness of Bernoulli processesMay 18 2013We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.

Multivariate Tail Estimation: Conditioning on an extreme eventFeb 25 2015We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral decomposition that allow ... More

Pathwise stochastic integration with finite variation processes uniformly approximating càdlàg processesNov 16 2012Apr 28 2013For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on compacts. The application ... More

New properties of a certain method of summation of generalized hypergeometric seriesFeb 29 2016Sep 05 2016In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the convergence ... More

Spin structures on flat manifoldsNov 28 2014Dec 19 2014We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.

The LIL for $U$-statistics in Hilbert spacesApr 12 2007We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, ... More

A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequalityMar 21 2014Dec 02 2015Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Lo\'{e}ve-Young inequality for the Riemann-Stieltjes ... More

Asymptotic distributions of Wishart type products of random matricesDec 21 2016Feb 16 2017We study asymptotic distributions of large dimensional random matrices of the form $BB^{*}$, where $B$ is a product of $p$ rectangular random matrices, using free probability and combinatorics of colored labeled noncrossing partitions. These matrices ... More

Small ball probability estimates in terms of widthJan 18 2005A certain inequality conjectured by Vershynin is studied. It is proved that for any $n$-dimensional symmetric convex body $K$ with inradius $w$ and $\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK) \leq (2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$. ... More

On Pathwise Uniform Approximation of Processes with Càdlàg Trajectories by Processes with Minimal Total VariationJun 16 2011Dec 08 2011For a real cadlag function $f$ and positive constant $c$ we find another cadlag function, which has the smallest total variation possible among the functions uniformly approximating f with accuracy c=2. The solution is expressed with the truncated variation, ... More

Interaction corrections at intermediate temperatures: magneto-resistance in parallel fieldSep 27 2001We consider the correction to conductivity of a 2D electron gas due to electron-electron interaction in the parallel magnetic field at arbitrary relation between temperature and the elastic mean free time. The correction exhibits non-trivial dependence ... More

Interaction corrections at intermediate temperatures: dephasing timeJan 22 2002Apr 02 2002We calculate the temperature dependence of the weak localization correction in a two dimensional system at arbitrary relation between temperature, $T$ and the elastic mean free time. We describe the crossover in the dephasing time ${\tau_\phi(T)}$ between ... More

Timing detectors for forward physicsMar 07 2019The use of precise time-of-flight (ToF) detectors for measurements of diffractive and electromagnetic processes in proton-proton collisions is discussed. The performance of background rejection exploiting the ToF measurements of the forward protons is ... More

On semi-exclusive measurement of $γγ\toγγ$ scatteringJul 07 2016The two-photon production of photon pairs, i.e. the $\gamma\gamma\to\gamma\gamma$ process, is studied. Different production modes regarding the elastic or inelastic coupling of the intermediate-state photons to the protons are considered. The semi-exclusive ... More