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Quantitative ergodicity for some switched dynamical systems. (English) Zbl 1347.60118
Summary: We provide quantitative bounds for the long time behavior of a class of piecewise deterministic Markov processes with state space \(\mathbb{R}^d\times E\), where \(E\) is a finite set. The continous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields, we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances.

MSC:
60J75 Jump processes (MSC2010)
60F99 Limit theorems in probability theory
60J25 Continuous-time Markov processes on general state spaces
93E15 Stochastic stability in control theory
34D23 Global stability of solutions to ordinary differential equations
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