Abstract
Let Y be an Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dYt=a(Xt)Yt dt+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.
Citation
Benoîte de Saporta. Jian-Feng Yao. "Tail of a linear diffusion with Markov switching." Ann. Appl. Probab. 15 (1B) 992 - 1018, February 2005. https://doi.org/10.1214/105051604000000828
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