Open AccessLimit theorems for asymptotic circular mth-order Markov chains indexed by an m-rooted homogeneous tree
Author(s) -
Huilin Huang,
Weiguo Yang
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1906817h
Subject(s) - mathematics , markov chain , limit (mathematics) , tree (set theory) , law of large numbers , homogeneous , sequence (biology) , corollary , order (exchange) , combinatorics , chain (unit) , markov process , discrete mathematics , mathematical analysis , random variable , statistics , finance , economics , physics , astronomy , biology , genetics
In this paper, we give the definition of an asymptotic circularmth-order Markov chain indexed by an m rooted homogeneous tree. By applying the limit property for a sequence of multi-variables functions of a nonhomogeneous Markov chain indexed by such tree, we estabish the strong law of large numbers and the asymptotic equipartition property (AEP) for asymptotic circular mth-order finite Markov chains indexed by this homogeneous tree. As a corollary, we can obtain the strong law of large numbers and AEP about the mth-order finite nonhomogeneous Markov chain indexed by the m rooted homogeneous tree.