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E. Ostrovsky

Publications and source records attributed to E. Ostrovsky.

At least 73 records · Page 4Linked to original sources
arXiv2015

Entropy and Grand Lebesgue Spaces approach for Prokhorov-Skorokhod continuity of random processes, with tail estimates

We present in this paper a new sufficient condition for the so-called Prokhorov-Skorokhod continuity of random processes. Our conditions will be formulated in the terms of metric entropy generated by three-dimensional distribution of the considered random process (r.p.) in the parametric set, have a convenient and closed form, and generalize some previous results. We study also the conditions for weak compactness of the sequence of random processes in this space and as a consequence the Central Limit Theorem. Our consideration based on the theory of Prokhorov-Skorokhod spaces of random processes and on the theory of Banach spaces of random variables with exponential decreasing tails of distributions, namely, on the theory of Grand Lebesgue Spaces (GLS) of random variables.

math.PR↗
arXiv2015

Fundamental function for Grand Lebesgue Spaces

We investigate in this short article the fundamental function for the so-called Grand Lebesgue Spaces (GLS) and show in particular a one-to-one and mutually continuous accordance between its fundamental and generating function.

math.FA↗
arXiv2015

Random processes and Central Limit Theorem in Besov spaces

We study sufficient conditions for the belonging of random process to certain Besov space and for the Central Limit Theorem (CLT) in these spaces. We investigate also the non-asymptotic tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces. Main apparatus is the theory of mixed (anisotropic) Lebesgue-Riesz spaces, in particular so-called permutation inequality.

math.PR↗
arXiv2015

Factorable continuity of random fields, with quantitative estimation

We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of continuity. We estimate also the ordinary and (possible) exponential moments of these random variables. We consider also the case of random fields with heavy tails of distribution and the so-called rectangle its continuity.

math.PR↗
arXiv2015

Problem of Estimation of Fractional Derivative for a Spectral Function of Gaussian Stationary Processes

We study the problem of nonparametric estimation of the fractional derivative of unknown spectral function of Gaussian stationary sequence (time series) and show that these problems is well posed with the classical speed of convergence when the order of derivative is less than 0.5. We prove also the asymptotical unbiaseness and normality of offered estimates with optimal speed of convergence. For the construction of the confidence region in some functional norm we establish the Central Limit Theorem in correspondent space of continuous functions for offered estimates.

math.ST↗
arXiv2015

Multidimensional Lusin-type inequalities for Grand Lebesgue Spaces

We generalize in this short paper the classical Luzin's theorem about existence of integral on the measurable function and its multidimensional analogues on the many popular classes of rearrangement invariant (r.i.) spaces, namely, on the so-called Grand Lebesgue Spaces.

math.FA↗
arXiv2014

Well Posedness of the Problem of Estimation Fractional Derivative for a Distribution Function

We study the problem of nonparametric estimation of the fractional derivative of unknown distribution function and of spectral function and show that these problems are well posed when the order of derivative is less than 0.5. We prove also the unbiaseness and asymptotical normality of offered estimates with optimal speed of convergence. For the construction of the confidence region in some functional norm we establish the Central Limit Theorem in correspondent Lebesgue-Riesz space for offered estimates, and deduce also the non-asymptotical deviation of our estimates in these spaces.

math.ST↗
arXiv2014

Sharp Lyapunov's inequality for the measurable sets with infinite measure, with generalization to the Grand Lebesgue spaces

We extend the classical Lyapunov inequality on the measurable space with infinite measure and on the so-called Grand Lebesgue spaces (GLS). We find also the exact value for correspondent constant. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables) etc.

math.FA↗
arXiv2014

Sharp moment estimates for polynomial martingales

In this paper non-asymptotic moment estimates are derived for tail of distribution for discrete time polynomial martingale by means of martingale differences as a rule in the terms of unconditional and unconditional relative moments and tails of distributions of summands. We show also the exactness of obtained estimations.

math.PR↗