Countable State Space Markov Random Fields and Markov Chains on Trees
نویسندگان
چکیده
منابع مشابه
Ergodic Theory for Countable State Space Markov Chains
Here we want to see to what extent the results from Doeblin’s theory for finite state spaces extend to the case when the state space is countably infinite. Throughout we will use π to denote the row vector whose jth component is πj = ( E[ρj |X0 = j] )−1. Theorem (A). If j is transient, then πj = 0 = limn→∞(P)ij for all i. Proof. Because P(ρj = ∞|X0 = j) > 0, it is clear that πj = 0. Thus, all t...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1983
ISSN: 0091-1798
DOI: 10.1214/aop/1176993439