Ratio Limit Theorems

David Freedman
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David Freedman: University of California, Department of Statistics

Chapter 2 in Markov Chains, 1983, pp 47-81 from Springer

Abstract: Abstract Throughout this chapter, unless noted otherwise, I is a recurrent class relative to the stochastic matrix P. Interest centers on the null recurrent case and on measures with infinite mass. Fix a reference state s ∈ I. Remember that {ξ n } is Markov with stationary transitions P and starting state s relative to the probability P 8 . Remember that the first s-block runs from the first s to just before the second s. Remember the definition (1.80) of invariance and subinvariance. Define the measure μ on I by the relation: μ(i) is the P 8 -mean number of i’s in the first s-block; that is, $$ \mu (i) = e\left( {P\left\{ s \right\}} \right)\left( {s,i} \right) = eP\left\{ s \right\}\left( {s,i} \right) $$

Date: 1983
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DOI: 10.1007/978-1-4612-5500-0_2

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