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Ratio limit theorems
for Markov chains
Sidney Charles Port |
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Vol. 15 (1965), No. 3, 989–1017
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Abstract |
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In an irreducible, recurrent, Markov chain, with integer states, let Nn(A) be the occupation time of A by time n, where A is a finite set of states. Our principal concern in this paper is to investigate various “ratio limit theorem” for Px(Nn(A) = k). Criteria are given for various ratio limits to exist. The limits (when they exist) are shown to be expressible in terms of an integral over the set of states E completed with its dual recurrent boundary B. Applications are given to several specific Markov chains. |
Mathematical Subject Classification
Primary: 60.65
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Milestones
Received: 15 September 1964
Published: 1 September 1965
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Authors |
| Sidney Charles Port | |
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