Open Access
Translator Disclaimer
2012 Quantitative ergodicity for some switched dynamical systems
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu, Pierre-André Zitt
Author Affiliations +
Electron. Commun. Probab. 17: 1-14 (2012). DOI: 10.1214/ECP.v17-1932


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 it 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.


Download Citation

Michel Benaïm. Stéphane Le Borgne. Florent Malrieu. Pierre-André Zitt. "Quantitative ergodicity for some switched dynamical systems." Electron. Commun. Probab. 17 1 - 14, 2012.


Accepted: 3 December 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1347.60118
MathSciNet: MR3005729
Digital Object Identifier: 10.1214/ECP.v17-1932

Primary: 60J75
Secondary: 34D23 , 60J25 , 93E15

Keywords: coupling , ergodicity , linear differential equations , Piecewise deterministic Markov process , Switched dynamical systems , Wasserstein distance


Back to Top