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Tail of a linear diffusion with Markov switching

Benoîte de Saporta 1 Jian-Feng Yao 1, 2 
2 VISTA - Vision spatio-temporelle et active
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : 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.
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Submitted on : Monday, April 21, 2008 - 4:47:52 PM
Last modification on : Friday, May 20, 2022 - 9:04:43 AM


  • HAL Id : hal-00274880, version 1


Benoîte de Saporta, Jian-Feng Yao. Tail of a linear diffusion with Markov switching. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 339 (9), pp.643-646. ⟨hal-00274880⟩



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