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Ergodic properties of generalized Ornstein--Uhlenbeck processes (1606.01232v1)
Published 3 Jun 2016 in math.PR
Abstract: We investigate ergodic properties of generalized Ornstein--Uhlenbeck processes. In particular, we provide sufficient conditions for ergodicity, and for subexponential and exponential convergence to the invariant probability measure. We use the Foster--Lyapunov method. The drift conditions are obtained using the explicit form of the generator of the continuous process. In some special cases the optimality of our results can be shown.