Advanced search
Start date
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

imit theorems for chains with unbounded variable length memory which satisfy Cramer condition{*

Full text
Logachov, A. [1, 2] ; Mogulskii, A. [1] ; Yambartsev, A. [3]
Total Authors: 3
[1] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Lab Probabil Theory & Math Stat, Koptuga 4, Novosibirsk 630090 - Russia
[2] Siberian State Univ Geosyst & Technol, Dept High Math, Plahotnogo Str 10, Novosibirsk 630108 - Russia
[3] Univ Sao Paulo, Inst Math & Stat IME USP, Dept Stat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: ESAIM-PROBABILITY AND STATISTICS; v. 26, p. 152-170, FEB 21 2022.
Web of Science Citations: 0

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. (AU)

FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Oswaldo Baffa Filho
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 17/20482-0 - Large deviations principle for stochastic processes
Grantee:Anatoli Iambartsev
Support Opportunities: Research Grants - Visiting Researcher Grant - International