## Electronic Communications in Probability

### Quantitative ergodicity for some switched dynamical systems

#### 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

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

Rights

#### 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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