Ecole d’Eté de Probabilités de Saint-Flour XI — 1981

We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel).We apply obtained results to the investigation of the local structure of random processes, for example, we find the necessary and sufficient condition for continuity of Gaussian and non-Gaussian processes, some conditions for weak compactness and convergence of a family of random processes, in particular, for Central Limit Theorem in the space of continuous functions.We give also many examples in order to illustrate the exactness of proved theorems.

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“…Another approach for the tail estimation for the maximum distribution of random field is closely related with notions "majorizing measures" or equally "generic chaining", see [8], [26], [27], [28], [2], [3], [60], [61] etc.…”

Section: Another Approachmentioning

confidence: 99%

Central limit theorem and exponential tail estimations in hybrid Lebesgue-continuous spaces

Ostrovsky,

Sirota

2013

Preprint

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Ecole d’Eté de Probabilités de Saint-Flour XI — 1981

Cited by 15 publications

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Non-asymptotical sharp exponential estimates for maximum distribution of discontinuous random fields

Non-asymptotical sharp exponential estimates for maximum distribution of discontinuous random fields

Theory of approximation and continuity of random processes

Central limit theorem and exponential tail estimations in hybrid Lebesgue-continuous spaces

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