Tail of a linear diffusion with Markov switching

2005/03/24 by Benoite de Saporta, Jian-Feng Yao
Mathematics · #math.PR #msc:60J60 #msc:60J75 #msc:60H25 #msc:60K05 #msc:60J15

paper · pdf · doi:10.1214/105051604000000828

published as Annals of Applied Probability 2005, Vol. 15, No. 1B, 992-1018 · Published at http://dx.doi.org/10.1214/105051604000000828 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2005/03/24 · arxiv updated 2009/12/01

Abstract

Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dY_t=a(X_t)Y_t dt+σ(X_t) dW_t, 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.

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