Tail of a linear diffusion with Markov switching

Details Tail of a linear diffusion with Markov switching Tail of a linear diffusion with Markov switching

2005-03-24

arxiv.org/abs/math/0503527v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 992-1018

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000828 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000828

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+\sigma(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.

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