The Key Renewal Theorem for a Transient Markov Chain

Details The Key Renewal Theorem for a Transient Markov Chain The Key Renewal Theorem for a Transient Markov Chain

2007-11-14

arxiv.org/abs/0711.2169v1

Mathematics

Probability

12 pages

Scientific paper

We consider a time-homogeneous Markov chain $X_n$, $n\ge0$, valued in ${\bf
R}$. Suppose that this chain is transient, that is, $X_n$ generates a
$\sigma$-finite renewal measure. We prove the key renewal theorem under
condition that this chain has asymptotically homogeneous at infinity jumps and
asymptotically positive drift.

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