Abstract
Let X n be a discrete parameter Markov process on general state space with transition functions P n (x, A). Individual ratio limit theorems are results about convergence as n→∞ of the ratios $$\frac{{P^{n + k} (x,A)}}{{P^n (y,B)}}$$ (1) where k is a fixed integer, A and B are subsets of state space, and x and y are starting points. This paper investigates the relationship of individual ratio limit theorems to various forms of asymptotic independence. When the state space is denumerable it is shown that, subject to standard auxiliary conditions, the much studied Strong Ratio Limit Property is equivalent to a form of asymptotic independence related to mixing conditions of Rosenblatt and Blum, Hanson, and Koopmans.
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More From: Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete
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