Tail of a linear diffusion with Markov switching

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.

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)

Cited by in corpus (6)

• Exponential ergodicity for Markov processes with random switching
• Quantitative ergodicity for some switched dynamical systems
• Probabilistic and Piecewise Deterministic models in Biology
• Large time behavior in random multiplicative processes
• A Central Limit Theorem for Punctuated Equilibrium
• Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchin