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R ‐Theory for Markov Chains on a Topological State Space I
Author(s) -
Pollard David B.,
Tweedie Richard L.
Publication year - 1975
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-10.4.389
Subject(s) - library science , citation , mathematics , statistics , sociology , computer science
~z"P"(x, A) of the n-step transition probabilities, we follow Tweedie [6] in using 1 the following form of irreducibility: there is a probcbility measure M on g for which M(A)>0 implies that G~(x,A)>O for all x~g, and M(A)=0 implies M{y: G~(y,A)>O}=O. We denote {A~,~: M(A)>0} by Y+; "almost all x" shall henceforth be with respect to this M. Tweedie [6] has proved the following solidarity results for such a chain (cs Theorems A and C of [4]):