Exponential ergodicity for Markov processes with random switching

摘要: We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, choice dynamics that changes at jump times second component. The is discrete and its rates may depend on position whole process. Under regularity assumptions Wasserstein contraction conditions for we provide concrete criterion convergence equilibrium in terms distance. proof based coupling argument weak form Harris theorem. In particular, obtain exponential ergodicity situations which do not verify any hypoellipticity assumption, but are uniformly contracting either. also bound total variation distance under suitable regularising assumption. Some examples given illustrate our result, including class piecewise deterministic processes.