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Research supported by the N.S.F. under grant GP 7128.
As usualP x {A}=P{A‖X o=x}, the conditional probability ofA, givenX o=x.
Note that by Lemma 2 of [6], (1.2) impliesf n/(1)>0 eventually. Thus the various ratios withf n (1) in the denominator are well defined for largen. (The condition (1.7) of [6] may be assumed valid; see beginning of sect. 2 below.)
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Kesten, H. A ratio limit theorem for symmetric random walk. J. Anal. Math. 23, 199–213 (1970). https://doi.org/10.1007/BF02795500
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DOI: https://doi.org/10.1007/BF02795500