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

Autor(es)

Logachov, A. ^{[1, 2]} ; Mogulskii, A. ^[1] ; Yambartsev, A. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: ESAIM-PROBABILITY AND STATISTICS; v. 26, p. 152-170, FEB 21 2022.
• Citações Web of Science: 0

Resumo

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)

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