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E. Ostrovsky

Publications and source records attributed to E. Ostrovsky.

At least 55 records · Page 3Linked to original sources
arXiv2018

Improved Monte-Carlo method for solving of integral Fredholm's equations of a second kind, with confidence regions in the uniform norm

We offer in this article some modification of Monte-Carlo method for solving of a linear integral Fredholm's equation of a second kind (Fredholm's well posed problem). We prove that the rate of convergence of offered method is optimal under natural conditions still in an uniform norm, and construct an asymptotic as well as non-asymptotic confidence region, again in the uniform norm.

math.NA↗
arXiv2018

Moment and tail estimation for U-statistics with positive kernels

We deduce the non-asymptotical (bilateral) estimates for moment inequalities for multiple sums of non-negative (more precisely, non-negative) independent random variables, on the other words, the well known U or V-statistics. Our consideration based on the correspondent estimates for the one-dimensional case by means of the so-called degenerate approximation. We apply also the theory of Bell functions as well as the properties of the Poisson distribution and the theory of the so-called Grand Lebesgue Spaces (GLS).

math.PR↗
arXiv2017

Inversion of Tchebychev-Tchernov inequality

We derive in this article the {\it lower} bound for tail of distribution for the random variables (r.v.) through a lower estimate for its moment generating functions (MGF).

math.PR↗
arXiv2017

Prokhorov-Skorokhod continuity of random fields. A natural approach

We derive in this article sufficient conditions in the natural terms for belonging of almost all the trajectories of the certain separable continuous in probability random field to the multivariate Prokhorov-Skorokhod space. We consider also as a consequence the Central Limit Theorem in this spaces.

math.PR↗
arXiv2017

Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields

We derive in this preprint the moment and exponential tail estimates, sufficient conditions for the Non-Central Limit Theorem (NCLT) in the ordinary one-dimensional space as well as in the space of continuous functions for the properly (natural) normalized multi-indexed sums of function of random variables, processes or fields (r.f.), on the other words V-statistics, parametric, in general case. We construct also some examples in order to show the exactness of obtained estimates. We will use the theory of the so-called degenerate approximation of the functions of several variables as well as the theory of Grand Lebesgue Spaces (GLS) of measurable functions (random variables).

math.PR↗
arXiv2017

Exact asymptotic for tail of distribution of self-normalized

We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of non-standard random norming function and the tail asymptotic for the maximum distribution for self-normalized statistics. We do not suppose the independence or identical distributionness of considered random variables, but we assume the existence and sufficient smoothness of its density. We show also the exactness of our conditions imposed on the considered random variables by means of building of an appropriate examples (counterexamples).

math.PR↗
arXiv2017

Maximal and other operators in exponential Orlicz and Grand Lebesgue Spaces

We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic rearrangement invariant norm: exponential Orlicz and Grand Lebesgue Spaces. We will use also the theory of the so-called Grand Lebesgue Spaces (GLS) of measurable functions.

math.FA↗
arXiv2016

Sharp value for the norm of composition and multiplicative operators between two different Grand Lebesgue spaces

We calculate in this paper the norm of composition, multiplicative and product operator, generated by multiplicative and measurable argument transformation between two different ordinary Lebesgue-Riesz and Grand Lebesgue spaces. We set ourselves the aim to obtain the exact expression for the norm of the considered operators by means of building of appropriate examples.

math.FA↗
arXiv2016

Uniform Limit Theorem and tail estimates for parametric u-statistics

We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also a non-asymptotic and non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for the uniform norm of centered and naturally normed deviation of u-statistics by means of its martingale representation. Our results are formulated in a very popular and natural terms of metric entropy in the distance (distances) generated by the introduced random processes (fields).

math.ST↗
arXiv2016

Sharp moment and exponential tail estimates for U-statistics

We obtain in this paper a non-asymptotic non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for U-statistics by means of martingale representation. We show also the exactness of obtained estimations in one way or another by providing appropriate examples.

math.ST↗
arXiv2016

Banach spaces characterization of random vectors with exponential decreasing tails of distribution

We present in this paper the Banach space representation for the set of random finite-dimensional vectors with exponential decreasing tails of distributions. We show that there are at last three types of these multidimensional Banach spaces, i.e. which can completely describe the random vectors with exponential decreasing tails of distributions: exponential Orlicz spaces, Young spaces and Grand Lebesgue spaces. We discuss in the last section the possible applications of obtained results.

math.PR↗