Chebyshev-Type Inequalities and Large Deviation Principles Full article
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Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219 |
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| Output data | Year: 2022, Volume: 66, Number: 4, Pages: 570 - 581 Pages count : 12 DOI: 10.1137/S0040585X97T990629 | ||
| Tags | exponential Chebyshev-type inequalitylarge deviation principlelocal large deviation principlerandom walkrandom fieldErd\Hos--Rényi graphs | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2016-0008 |
Abstract:
Let ξ1,ξ2,… be a sequence of independent copies of a random variable (r.v.) ξ, Sn=∑nj=1ξj, A(λ)=lnEeλξ, Λ(α)=supλ(αλ−A(λ)) is the Legendre transform of A(λ). In this paper, which is partially a review to some extent, we consider generalization of the exponential Chebyshev-type inequalities P(Sn≥αn)≤exp{−nΛ(α)}, α≥Eξ, for the following three cases: I. Sums of random vectors, II. stochastic processes (the trajectories of random walks), and III. random fields associated with Erd\Hos--Rényi graphs with weights. It is shown that these generalized Chebyshev-type inequalities enable one to get exponentially unimprovable upper bounds for the probabilities to hit convex sets and also to prove the large deviation principles for objects mentioned in I--III.
Cite:
Borovkov A.A.
, Logachov A.V.
, Mogulʹskii A.A.
Chebyshev-Type Inequalities and Large Deviation Principles
Theory of Probability and its Applications. 2022. V.66. N4. P.570 - 581. DOI: 10.1137/S0040585X97T990629 WOS Scopus РИНЦ OpenAlex
Chebyshev-Type Inequalities and Large Deviation Principles
Theory of Probability and its Applications. 2022. V.66. N4. P.570 - 581. DOI: 10.1137/S0040585X97T990629 WOS Scopus РИНЦ OpenAlex
Original:
Боровков А.А.
, Логачев А.В.
, Могульский А.А.
Неравенства чебышёвского типа и принципы больших уклонений
Теория вероятностей и ее применения. 2021. Т.66. №4. С.718–733. DOI: 10.4213/tvp5498 РИНЦ OpenAlex
Неравенства чебышёвского типа и принципы больших уклонений
Теория вероятностей и ее применения. 2021. Т.66. №4. С.718–733. DOI: 10.4213/tvp5498 РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000752423100006 |
| Scopus: | 2-s2.0-85129682227 |
| Elibrary: | 48583077 |
| OpenAlex: | W4213458593 |