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Tail of a linear diffusion with Markov switching

Benoite de Saporta·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: 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.

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Benoite de Saporta, Jian-Feng Yao. 2005-03-24. Tail of a linear diffusion with Markov switching. https://doi.org/10.1214/105051604000000828

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