Let Y be an Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dYt=a(Xt)Yt dt+σ(Xt) dWt, Y0=y0. Ergodicity conditions for Y have been obtained. Here we investigate the tail propriety of the stationary distribution of this model. A characterization of either heavy or light tail case is established. The method is based on a renewal theorem for systems of equations with distributions on ℝ.
Publié le : 2005-02-14
Classification:
Ornstein–Uhlenbeck diffusion,
Markov switching,
random difference equation,
light tail,
heavy tail,
renewal theory,
Perron–Frobenius theory,
ladder heights,
60J60,
60J75,
60H25,
60K05,
60J15
@article{1107271676,
author = {de Saporta, Beno\^\i te and Yao, Jian-Feng},
title = {Tail of a linear diffusion with Markov switching},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 992-1018},
language = {en},
url = {http://dml.mathdoc.fr/item/1107271676}
}
de Saporta, Benoîte; Yao, Jian-Feng. Tail of a linear diffusion with Markov switching. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 992-1018. http://gdmltest.u-ga.fr/item/1107271676/