On the Existence Conditions for Exact Large Deviation Principles Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2022, Volume: 63, Number: 1, Pages: 48-64 Pages count : 17 DOI: 10.1134/S0037446622010049 | ||
| Tags | 519.21; exact large deviation principle; extended large deviation principle; large deviation principle; random walks; renewal compound processes; thin boundaries | ||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | 0314-2016-0008 |
| 2 | Russian Foundation for Basic Research | 18-01-00101-a |
Abstract:
We consider large deviation principles (LDPs) for random walksand renewal compound processes.We expose and analyze the approaches tofinding existence conditions for“exact” large deviation principlesvalid under minimal moment conditions.By exact large deviation principles we understandstatements on the existence of exact limitsfor the asymptotics of the probabilities under studyand the values of these limitsrather than on the existence of upper and lower limits for these asymptotics,as for the ordinary large deviation principles.In addition to the known results,the new versions of conditions are found thatensure the existence of exact LDPs under the minimal Cramér’s moment condition.The article is based on the text of a talkprepared for a conference cancelled because of the pandemic. © 2022, Pleiades Publishing, Ltd.
Cite:
Borovkov A.A.
On the Existence Conditions for Exact Large Deviation Principles
Siberian Mathematical Journal. 2022. V.63. N1. P.48-64. DOI: 10.1134/S0037446622010049 WOS Scopus РИНЦ OpenAlex
On the Existence Conditions for Exact Large Deviation Principles
Siberian Mathematical Journal. 2022. V.63. N1. P.48-64. DOI: 10.1134/S0037446622010049 WOS Scopus РИНЦ OpenAlex
Original:
Боровков А.А.
Об условиях существования точных принципов больших уклонений
Сибирский математический журнал. 2022. Т.63. №1. С.58–76. DOI: 10.33048/smzh.2022.63.104 РИНЦ MathNet
Об условиях существования точных принципов больших уклонений
Сибирский математический журнал. 2022. Т.63. №1. С.58–76. DOI: 10.33048/smzh.2022.63.104 РИНЦ MathNet
Identifiers:
| Web of science: | WOS:000749276800004 |
| Scopus: | 2-s2.0-85123634522 |
| Elibrary: | 48145964 |
| OpenAlex: | W4210746872 |