Comptes Rendus
Probability Theory
Tail of a linear diffusion with Markov switching
Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 643-646.

Let Y be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X, i.e. dYt=a(Xt)Ytdt+σ(Xt)dWt, Y0=y0. Ergodicity conditions for Y have been obtained. Here we investigate the tail property of the stationary distribution of this model. A characterization of the only two possible cases is established: light tail or polynomial tail. Our method is based on discretizations and renewal theory.

Soit Y une diffusion de Ornstein–Uhlenbeck dirigée par un processus Markovien de saut X stationnaire et ergodique : dYt=a(Xt)Ytdt+σ(Xt)dWt, Y0=y0. On connaît des conditions d'ergodicité pour Y. Ici on s'intéresse à la queue de la loi stationnaire de ce modèle. Par des méthodes de discrétisation et de renouvellement, on donne une caractérisation complète des deux seuls cas possibles : queue polynômiale ou existence de moment à tout ordre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.09.022

Benoîte de Saporta 1; Jian-Feng Yao 1

1 IRMAR, université de Rennes I, campus de Beaulieu, 35042 Rennes cedex, France
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Benoîte de Saporta; Jian-Feng Yao. Tail of a linear diffusion with Markov switching. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 643-646. doi : 10.1016/j.crma.2004.09.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.022/

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