Electronic Communications in Probability

Quantitative ergodicity for some switched dynamical systems

Michel Benaïm, Stéphane Le Borgne, Florent Malrieu, and Pierre-André Zitt

Full-text: Open access

Abstract

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.

Article information

Source
Electron. Commun. Probab. Volume 17 (2012), paper no. 56, 14 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263189

Digital Object Identifier
doi:10.1214/ECP.v17-1932

Mathematical Reviews number (MathSciNet)
MR3005729

Zentralblatt MATH identifier
1347.60118

Subjects
Primary: 60J75: Jump processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces 93E15: Stochastic stability 34D23: Global stability

Keywords
Coupling Ergodicity Linear Differential Equations Piecewise Deterministic Markov Process Switched dynamical systems Wasserstein distance

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Benaïm, Michel; Le Borgne, Stéphane; Malrieu, Florent; Zitt, Pierre-André. Quantitative ergodicity for some switched dynamical systems. Electron. Commun. Probab. 17 (2012), paper no. 56, 14 pp. doi:10.1214/ECP.v17-1932. https://projecteuclid.org/euclid.ecp/1465263189.


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