Results for "Nikolai Lauk"
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Optimal replication of random vectors by ordinary integralsAug 07 2012Aug 08 2012We consider a problem of replication of random vectors by ordinary integrals in the setting when a underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral at a fixed ... More Controlled options: derivatives with added flexibilityDec 07 2010Oct 14 2011The paper introduces a limit version of multiple stopping options such that the holder selects dynamically a weight function that control the distribution of the payments (benefits) over time. In applications for commodities and energy trading, a control ... More Bottom Quark Mass from $Υ$ Sum Rules to ${\cal O}(α_s^3)$Jun 30 2014We present the deterimination of the bottom quark mass using non-relativistic $\Upsilon$ Sum Rules at $\text{N}^3\text{LO}^*$[1]. The explicit dependence of $\overline{m}_b(\overline{m}_b)$ on the input value $\alpha_s(M_Z)$ is given for the first time. ... More On the nature of QPO phase lags in black hole candidatesMay 03 2012Observations of quasi-periodic oscillations (QPOs) in X-ray binaries hold a key to understanding many aspects of these enigmatic systems. Complex appearance of the Fourier phase lags related to QPOs is one of the most puzzling observational effects in ... More A complete closed-form solution to a tropical extremal problemOct 12 2012A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two other known problems ... More On recovering missing values in a pathwise settingApr 18 2016Apr 21 2016The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e., discrete time processes, in a pathwise setting, without using probabilistic assumptions on the ensemble. This setting targets situations where ... More On sub-ideal causal smoothing filtersDec 29 2010Jul 12 2011Smoothing causal linear time-invariant filters are studied for continuous time processes. The paper suggests a family of causal filters with almost exponential damping of the energy on the higher frequencies. These filters are sub-ideal meaning that a ... More Two remarks on the Suita conjectureNov 24 2014It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1+\varepsilon_-}$-smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely ... More Existence of Dirac Eigenvalues of higher MultiplicityApr 04 2015In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by catching the desired ... More QCD Corrections in Gamma_sl(B)Oct 30 2002Dec 31 2002Short-distance expansion of the total semileptonic B widths is reviewed for the OPE-conformable scheme employing low-scale running quark masses. The third- and fourth-order BLM corrections are given and the complete resummation of the BLM series presented. ... More Recent Advances in Semileptonic B DecaysSep 09 2003Aspects of the OPE-based QCD theory of B decays are discussed. We have at least one nontrivial precision check of the OPE at the nonperturbative level in inclusive decays. The data suggest proximity to the `BPS' limit for B mesons. Its consequences are ... More Glueball dynamics in the hot plasmaJan 20 2016Apr 20 2016We discuss the glueball contribution to the equation of state (EoS) of hot gluon matter below and above $T_c$. It is shown that the strong changing of masses of scalar and pseudoscalar glueballs near $T_c$ plays very important role in the thermodynamics ... More Stochastic Theory of Foreign Exchange Market DynamicsSep 29 1999A new stochastic theory of a foreign exchange markets dynamics is developed. As a result we have the new probability distribution which well describes statistical and scaling dependencies ''experimentally'' observed in foreign exchange markets in recent ... More Classifying Vectoids and Generalisations of OperadsMay 16 2011A new generalisation of the notion of space, called "vectoid", is suggested in this work. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated properties not used ... More On recovering parabolic diffusions from their time-averagesSep 07 2016Oct 11 2016The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed ... More First Order BSPDEs: examples in higher dimensionMar 22 2016May 17 2016The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations)suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman equations and allow ... More Universal estimate of the gradient for parabolic equationsSep 06 2007Apr 29 2008We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient. More precisely, we found the upper limit estimate ... More On the no-arbitrage market and continuity in the Hurst parameterSep 22 2015Oct 13 2015We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we ... More Continuity of Dirac SpectraMar 26 2013It is a well-known fact that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article we extend this result to a global version. We ... More Strong interaction effects in semileptonic B decaysOct 02 2002Strong interaction effects are addressed in connection to extracting |V_{cb}|. A comprehensive approach is described not relying on a 1/m_c expansion; it allows a percent accuracy without ad hoc assumptions about higher-order effects. An alternative to ... More Topics in the Heavy Quark ExpansionOct 30 2000Nov 06 2000Achievements in the heavy quark theory over the last decade are reviewed, with the main emphasis put on dynamical methods which quantify nonperturbative effects via application of the Operator Product Expansion. These include the total weak decay rates ... More On detecting the dependence of time seriesOct 13 2010This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires to compare ... More Real and complex k-planes in convex hypersurfacesAug 23 2012It is shown that that the rank of the second fundamental form (resp. the Levi form) of a $\mathcal C^2$-smooth convex hypersurface $M$ in $\Bbb R^{n+1}$ (resp. $\Bbb C^{n+1}$) does not exceed an integer constant $k<n$ near a point $p\in M,$ then through ... More The 2D Zakharov-Kuznetsov-Burgers equation on a stripApr 17 2014An initial-boundary value problem for the 2D Zakharov-Kuznetsov-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small ... More Kawahara-Burgers equation on a stripAug 25 2014An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions ... More Sub-ideal causal smoothing filters for real sequencesNov 27 2014Jul 04 2015The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal smoothing ... More On causal band-limited mean square approximationNov 29 2011Aug 10 2012We study causal dynamic approximation of non-bandlimited processes by band-limited processes such that a part of the historical path of the underlying process is approximated in $L_2$-norm by the trace of a band-limited process. This allows to cover the ... More On identity theorem for real functionsNov 04 2009Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures similar property. ... More Graph-truncations of $3$-polytopesJan 15 2015In this paper we study the operation of cutting off edges of a simple $3$-polytope $P$ along the graph $\Gamma$. We give the criterion when the resulting polytope is simple and when it is flag. As a corollary we prove the analog of Eberhard's theorem ... More On sampling theorem with sparse decimated samplesMay 02 2016Nov 20 2016The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function is uniquely defined by infinite two-sided sampling series taken with a sufficient frequency. The paper shows that these band-limited functions ... More Dirac Eigenvalues of higher MultiplicityJan 16 2015Let M be a closed spin manifold of dimension at least three with a fixed topological spin structure. For any Riemannian metric, we can construct the associated Dirac operator. The spectrum of this Dirac operator depends on the metric of course. In 2005, ... More QCD in beauty decays: successes and puzzlesJun 08 2004The status of the heavy quark expansion for inclusive B decays is briefly reviewed from the perspective of confronting theory with data and of extracting the heavy quark parameters. A good agreement between properly applied theory and new precision data ... More A "BPS expansion" for B and D mesonsNov 30 2003We analyze consequences of the approximation \mu_\pi^2 -\mu_G^2 << \mu_\pi^2 (a `BPS' limit) for B and D mesons. It is shown that neglecting perturbative effects many power corrections would vanish to all orders in 1/m_Q, in particular those violating ... More On $L_1$-distance between first exit times from two regionsMar 20 2003First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of $L_1$-distance between exit times from two regions via expectations of exit times. A solution of a tropical linear vector equationDec 26 2012A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation ... More On exact and optimal recovering of a single missing valueApr 24 2016Aug 16 2016The paper studies frequency criterions of recoverability of a single missing value from an observed sequence. Stochastic Gaussian stationary processes that are non recoverable in this sense are called minimal processes; they have a degenerate spectral ... More On the homology cobordism group of homology 3-spheresAug 31 1996In this paper we present our results on the homology cobordism group $\Th$ of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by Donaldson and ... More Regularity of a inverse problem for generic parabolic equationsAug 31 2007The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary value inputs.