The Annals of Applied Probability

Tail of a linear diffusion with Markov switching

Benoîte de Saporta and Jian-Feng Yao

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Abstract

Let Y be an Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dYt=a(Xt)Ytdt+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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 1B (2005), 992-1018.

Dates
First available in Project Euclid: 1 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1107271676

Digital Object Identifier
doi:10.1214/105051604000000828

Mathematical Reviews number (MathSciNet)
MR2114998

Zentralblatt MATH identifier
1064.60174

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 60J75: Jump processes 60H25: Random operators and equations [See also 47B80]
Secondary: 60K05: Renewal theory 60J15

Keywords
Ornstein–Uhlenbeck diffusion Markov switching random difference equation light tail heavy tail renewal theory Perron–Frobenius theory ladder heights

Citation

de Saporta, Benoîte; Yao, Jian-Feng. Tail of a linear diffusion with Markov switching. Ann. Appl. Probab. 15 (2005), no. 1B, 992--1018. doi:10.1214/105051604000000828. https://projecteuclid.org/euclid.aoap/1107271676


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