Motivated by multivariate random recurrence equations we prove a new analogue
of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit
of Kesten [Ann. Probab. 2 (1974) 355--386].
Compactness of the state space and a certain continuity condition allows us to simplify
Kesten's proof considerably.
Publié le : 2003-10-14
Classification:
Key Renewal Theorem,
Markov chain,
random recurrence equation,
Riemann integrability,
60J05,
60K05,
60K15,
60H25
@article{1068646385,
author = {Kl\"uppelberg, Claudia and Pergamenchtchikov, Serguei},
title = {Renewal theory for functionals of a Markov chain with compact state space},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 2270-2300},
language = {en},
url = {http://dml.mathdoc.fr/item/1068646385}
}
Klüppelberg, Claudia; Pergamenchtchikov, Serguei. Renewal theory for functionals of a Markov chain with compact state space. Ann. Probab., Tome 31 (2003) no. 1, pp. 2270-2300. http://gdmltest.u-ga.fr/item/1068646385/