On the asymptotic events of a Markov chain

International Journal of Mathematics and Mathematical Sciences

HarryCohn¹ 

[1] Department of Statistics, University of Melbourne, Parkville 3052, Victoria, Australia;

关键词: tail σ;    -field;    invariant σ;    -field;    atomic set;    completely nonatomic set;    harmonic function;    space-time harmonic function;    martingale;    Martin boundary;    Chacon-Ornstein ergodic theorem;    0−;    2 Laws.;   

DOI  :  10.1155/S0161171279000430

来源: DOAJ

【 摘 要 】

In this paper we investigate some structure properties of the tail σ-field and the invariant σ-field of both homogeneous and nonhomogeneous Markov chains as representations for asymptotic events, descriptions of completely nonatomic and atomic sets and global characterizations of asymptotic σ-fields. It is shown that the Martin boundary theory can provide a unified approach to the asymptotic σ-fields theory.

【 授权许可】

Unknown