For a Harris recurrent Markov chain with invariant initial distribution $\pi$, we consider the return times $\tau_\varepsilon$ to state sets $A_\varepsilon$ with $0 < \pi(A_\varepsilon) \rightarrow 0$ as $\varepsilon \rightarrow 0$ and show that, provided the probability of early returns to $A_\varepsilon$ approaches 0, the $\tau_\varepsilon$, multiplied by suitable scaling factors, are asymptotically exponentially distributed.
Publié le : 1985-11-14
Classification:
First passage times,
return times,
Harris recurrent Markov chains,
state sets of small probability,
exponential distribution,
60J05,
60G10,
60K05,
60E05,
60F05
@article{1176992806,
author = {Cogburn, Robert},
title = {On the Distribution of First Passage and Return Times for Small Sets},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 1219-1223},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992806}
}
Cogburn, Robert. On the Distribution of First Passage and Return Times for Small Sets. Ann. Probab., Tome 13 (1985) no. 4, pp. 1219-1223. http://gdmltest.u-ga.fr/item/1176992806/