Tail of a linear diffusion with Markov switching

Benoîte de Saporta; Jian-Feng Yao

hal-00274874, version 1

Tail of a linear diffusion with Markov switching

Benoîte de Saporta () ^{1, 2, 3, 4}, Jian-Feng Yao ^1, 5

Annals of Applied Probability 15, 1B (2005) 992-1018

Abstract: 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 .

1: Institut de Recherche Mathématique de Rennes (IRMAR)
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
2: CQFD (INRIA Bordeaux - Sud-Ouest)
INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251
3: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
4: Groupe de Recherche en Economie Théorique et Appliquée (GREThA)
CNRS : UMR5113 – Université Montesquieu - Bordeaux IV
5: VISTA (INRIA - IRISA)
CNRS : UMR6074 – INRIA – Université de Rennes 1 – Institut National des Sciences Appliquées (INSA)

hal-00274874, version 1
http://hal.archives-ouvertes.fr/hal-00274874
oai:hal.archives-ouvertes.fr:hal-00274874
From: Benoîte De Saporta <>
Submitted on: Monday, 21 April 2008 16:40:50
Updated on: Monday, 22 March 2010 15:14:32

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DOI: 10.1214/105051604000000828

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