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Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition Full article

Journal ESAIM - Probability and Statistics
ISSN: 1292-8100 , E-ISSN: 1262-3318
Output data Year: 2022, Volume: 26, Pages: 152-170 Pages count : 19 DOI: 10.1051/ps/2022002
Tags Compound renewal process; Cramer condition; Large deviation principle; Local limit theorem; Moderate deviation principle; Rate function; Regeneration scheme; Variable length memory chain
Authors Logachov A. 1,2 , Mogulskii A. 1 , Yambartsev A. 3
Affiliations
1 Laboratory of Probability Theory and Mathematical Statistics, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Koptuga, 4, Novosibirsk, 630090, Russian Federation
2 Department of High Mathematics, Siberian State University of Geosystems and Technologies, Plahotnogo str. 10, Novosibirsk, 630108, Russian Federation
3 Department of Statistics, Institute of Mathematics and Statistics (IME-USP), University of São Paulo, Rua do Matão 1010, SP, São Paulo, CEP 05508-090, Brazil

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0010

Abstract: We consider a class of variable length Markov chains with a binary alphabet in which context tree is defined by adding finite trees with uniformly bounded height to the vertices of an infinite comb tree. Such type of Markov chain models the spike neuron patterns and also extends the class of persistent random walks. The main interest is the limiting properties of the empirical distribution of symbols from the alphabet. We obtain the strong law of large numbers, central limit theorem, and exact asymptotics for large and moderate deviations. The presence of an intrinsic renewal structure is the subject of discussion in the literature. Proofs are based on the construction of a renewals of the chain and the applying corresponding properties of the compound (or generalized) renewal processes. © The authors. Published by EDP Sciences SMAI 2022.
Cite: Logachov A. , Mogulskii A. , Yambartsev A.
Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition
ESAIM - Probability and Statistics. 2022. V.26. P.152-170. DOI: 10.1051/ps/2022002 WOS Scopus РИНЦ OpenAlex
Identifiers:
Web of science: WOS:000758368000001
Scopus: 2-s2.0-85125446362
Elibrary: 48186617
OpenAlex: W2982840465
Citing: Пока нет цитирований
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