Mixed ratio limit theorems for Markov processes

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2 Scopus citations

Abstract

Let P be a conservative and ergodic Markov operator on L1(X, Σ, m). We give a sufficient condition for the existence of a decomposition Af ↑X such that for 0≦f, g ∈L (Aj) and any two probability measures μ and ν weaker than m(Formula presented.), where λ is the σ-finite invariant measure (which necessarily exists). Processes recurrent in the sense of Harris are shown to have this decomposition, and an analytic proof of the convergence of(Formula presented.) is deduced for such processes.

Original languageEnglish
Pages (from-to)357-366
Number of pages10
JournalIsrael Journal of Mathematics
Volume8
Issue number4
DOIs
StatePublished - 1 Jan 1970
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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