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E. Ostrovsky

Publications and source records attributed to E. Ostrovsky.

At least 127 records · Page 7Linked to original sources
arXiv2012

Moment and tail estimates for martingales and martingale transform, with application to the martingale limit theorem in Banach spaces

In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale and martingale transform by means of martingale differences in the terms of moments and tails of distributions of summands and multipliers. We show also the exactness of obtained estimations and consider some applications in the theory of limit theorem for Banach space valued martingales.

math.PR↗
arXiv2011

Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications

We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some applications in the method Monte-Carlo and statistics, and obtain the sufficient conditions for Central and stable limit theorem in the Banach space of continuous function. There are considered a slight generalization on a random variables with super-heavy tails and martingale difference scheme.

math.PR↗
arXiv2011

Cpmposed Grand Lebesgue Spaces

In this article we introduce and investigate a new class of rearrangement invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are some generalizations of known Grand Lebesgue Spaces (GLS). We consider the fundamental functions of CGLS, calculate its Boyd's indices, obtain the norm boundedness some (regular and singular) operators in this spaces, investigate the conjugate and associate spaces, show that CGLS obeys the absolute continuous norm property etc.

math.FA↗
arXiv2011

Adaptive Optimal Signal (Cardiogram) Processing, with boundary values and energy precisely measurement

We construct an adaptive asymptotically optimal in order in the weight Hilbert space norms signal denoising on the background noise and its energy measurement, with hight precision near the boundary of the signal. An offered method used the Fourier-Riesz expansion on the orthonormal polynomials, for instance, Jacobi's polynomials, relative unbounded near the boundary weight function. An applications: technical and medical, in particular, cardiac diagnosis.

math.ST↗
arXiv2011

Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm

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

math.FA↗
arXiv2010

Wirtinger-type inequalities for some rearrangement invariant spaces

In this short paper we generalize the classical inequality between the norms in Lebesgue spaces of the functions and its derivatives, which in the multidimensional case are called Sobolev's inequalities, on the many popular classes pairs of rearrangement invariant (r.i.) spaces, namely, on the so-called moment rearrangement invariant spaces.

math.FA↗
arXiv2009

Integral Operators in Bilateral Grand Lebesgue Spaces

In this paper we estimate the norm of operator acting from one Bilateral Grand Lebesgue Space (BGLS) into other Bilateral Grand Lebesgue Space. We also give some examples to show the sharpness of offered inequalities.

math.FA↗
arXiv2009

Poincaré Inequalities in Bilateral Grand Lebesgue Spaces

In this paper we obtain the non - asymptotic estimations of Poincare type between function and its gradient in the so - called Bilateral Grand Lebesgue Spaces. We also give some examples to show the sharpness of these inequalities.

math.FA↗