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Journal Article

On the Distribution of First Passage and Return Times for Small Sets

Robert Cogburn
The Annals of Probability
Vol. 13, No. 4 (Nov., 1985), pp. 1219-1223
Stable URL: http://www.jstor.org/stable/2244173
Page Count: 5

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Topics: Markov chains, Mathematical theorems, Ergodic theory, Mathematics, Neys

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For a Harris recurrent Markov chain with invariant initial distribution π, we consider the return times τε to state sets Aε with $0 < \pi(A_\varepsilon) \rightarrow 0$ as ε → 0 and show that, provided the probability of early returns to Aε approaches 0, the τε, multiplied by suitable scaling factors, are asymptotically exponentially distributed.