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Invariant Measures for Path-Dependent Random Diffusions

  • Speaker: Jinghai Shao(Tianjin University)

  • Time: Oct 19, 2017, 10:40-11:30

  • Location: Conference Room 415, Wisdom Valley 3#

In this talk, we are concerned with existence and uniqueness of invariant measures for pathdependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment characterized by a continuous time Markov chain. Under certain ergodic conditions, we show that the path-dependent random diffusion enjoys a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also, we demonstrate that the time discretization of the pathdependent random diffusion involved admits a unique invariant probability measure and shares the corresponding ergodic property when the stepsize is sufficiently small. During this procedure, the difficulty arose from the time-discretization of continuous time Markov chain has to be deal with, for which an estimate on its exponential functional is presented.