Tail of a linear diffusion with Markov switching

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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, Y_0=y_0. 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.
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)

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Probability, 60J60, 60J75, 60H25 (Primary) 60K05, 60J15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/74625

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503527
 http://arxiv.org/abs/math/0503527
 Annals of Applied Probability 2005, Vol. 15, No. 1B, 992-1018
 doi:10.1214/105051604000000828

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arXiv