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E. Ostrovsky

Publications and source records attributed to E. Ostrovsky.

At least 91 records · Page 5Linked to original sources
arXiv2014

Central Limit Theorem in Holder spaces in the terms of majorizing measures

We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and M.Talagrand. We introduce a new class of Banach spaces-rectangle Holder spaces and investigate CLT in this spaces via the fractional order Sobolev-Grand Lebesgue norms. Our further considerations based on the improvement of the L.Arnold and P.Imkeller generalization of the classical Garsia-Rodemich-Rumsey inequality, which allow us to reduce degree of the distance in the important particular cases.

math.PR↗
arXiv2014

A simple Monte Carlo method for solving of Navier-Stokes Equations

We offer a simple Monte-Carlo method for solving of the multidimensional initial value and non-homogeneous problem for the Navier-Stokes Equations in whole space when the initial function and right hand side belong to the correspondent Sobolev-Lebesgue-Riesz space.

math.NA↗
arXiv2014

Lower boundaries for parametric estimations in different norms

We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is weaker that ordinary Hilbertian norm, that the rate of convergence of arbitrary regular unbiased estimate does not exceed $ 1/\sqrt{n}, $ and if the new norm is stronger that one, the rate of convergence of the well-known Maximal Likelihood Estimate (MLE) is also equal to $ 1/\sqrt{n}.

math.ST↗
arXiv2014

The rate of increase for recursion with quadratic non-linearity

We investigate in this short report the rate of increase of positive numerical recursion with quadratic non-linearity. More exactly, we intent to calculate the logarithmic index of its increasing. We present also the possible application in the theory of the Navier-Stokes equations.

math.GM↗
arXiv2014

Monte Carlo computation of multiple weak singular integrals of spherical and Volterra's type

We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density, and we offer a highly effective way for generation of appeared multidimensional distribution. We extend offered method onto multiple Volterra's and spherical integrals with weak singularities containing parameter.

math.NA↗
arXiv2014

Lebesgue-Riesz norm estimates for fractional Laplace transform

We obtain in this short article the bilateral non-asymptotic estimations for the norm in Lebesgue-Riesz and bilateral Grand Lebesgue spaces of the so-called fractional Laplace integral transform. We give also examples to show the sharpness of these inequalities.

math.FA↗
arXiv2014

Exact exponential tail estimations in the Law of Iterated Logarithm for Bochner's mixed Lebesgue spaces

We obtain the quite exact exponential bounds for tails of distributions of sums of Banach space valued random variables uniformly over the number of summands under natural for the Law of Iterated Logarithm (LIL) norming. We study especially the case of the so-called mixed (anisotropic) Lebesgue-Riesz spaces, on the other words, Bochner's spaces, for instance, continuous-Lebesgue spaces, which appear for example in the investigation of non-linear Partial Differential Equations of evolutionary type. We give also some examples in order to show the exactness of our estimates.

math.PR↗
arXiv2014

Sufficient conditions for exponential tightness of normed sums of independent random fields in the space of continuous functions

We formulate and prove in this report some sufficient conditions for exponential tightness (ET) of a family of independent identical distributed (i.i.d.) random fields (r.f.) (processes) in the space of continuous functions defined on certain metric compact set. We will use the entropic method as well as too modern approach through the majorizing measures (generic chaining).

math.PR↗
arXiv2014

Uniform measures on the arbitrary compact metric spaces, with applications

We introduce and investigate in this short report the new notion of uniform measure (distribution) on the arbitrary compact metric space. We consider also some possible applications of these measures in the theory of imbedding theorems and in the theory of random processes (fields), in particular, in the so-called majorizing (and minorizing) measures method, belonging to X.Fernique and M.Talagrand. These considerations based on the L.Arnold and P.Imkeller generalization of the classical A.M.Garsia-E.Rodemich-H.Jr.Rumsey inequality and X.Fernique-M.Talagrand estimation for random fields.

math.FA↗
arXiv2013

Parametric density-based optimization of partition in cluster analysis, with applications

We developed an optimal in the natural sense algorithm of partition in cluster analysis based on the densities of observations in the different hypotheses. These densities may be characterized, for instance, as the multivariate so-called "quasi-Gaussian distribution". We describe also the possible applications in technical diagnosis, demography and philology.

math.ST↗
arXiv2013

Characterization of quasy-Gaussian distributions

A new characterization of the multivariate so-called "quasi-Gaussian distribution" (the authors dared to coin a new term) by means of independence their Cartesian and polar coordinates proposed. The authors try to show that these distributions may essentially differ from the classical Gaussian distribution. Some properties of these distributions are studied: calculating of moments and of bilateral tail behavior. Some potential applications of these distributions and mixtures of the distributions in demography, philology are discussed in the final section.

math.ST↗