Invariant measures for Markov chains with no irreducibility assumptions
Invariant measures for Markov chains with no irreducibility assumptions
复制标题
DOI：
10.2307/3214162
复制
发表时间：
1988
影响因子：
1
通讯作者：
R. Tweedie
中科院分区：
文献类型：
--
作者：
R. Tweedie
Foster's criterion for positive recurrence of irreducible countable space Markov chains is one of the oldest tools in applied probability theory. In various papers in JAP and AAP it has been shown that, under extensions of irreducibility such as ϕ -irreducibility, analogues of and generalizations of Foster's criterion give conditions for the existence of an invariant measure π for general space chains, and for π to have a finite f-moment ∫π (dy)f(y), where f is a general function. In the case f ≡ 1 these cover the question of finiteness of π itself. In this paper we show that the same conditions imply the same conclusions without any irreducibility assumptions; Foster's criterion forces sufficient and appropriate regularity on the space automatically. The proofs involve detailed consideration of the structure of the minimal subinvariant measures of the chain. The results are applied to random coefficient autoregressive processes in order to illustrate the need to remove irreducibility conditions if possible.
