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 Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches 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. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.
Document type :
Journal articles
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download

Contributor : Pierre-André Zitt <>
Submitted on : Wednesday, December 5, 2012 - 11:24:55 PM
Last modification on : Wednesday, November 28, 2018 - 2:48:22 PM
Long-term archiving on: Saturday, December 17, 2016 - 9:17:36 PM


Files produced by the author(s)



Michel Benaïm, Stéphane Le Borgne, Florent Malrieu, Pierre-André Zitt. Quantitative ergodicity for some switched dynamical systems. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2012, 17 (56), pp.1-14. ⟨10.1214/ECP.v17-1932⟩. ⟨hal-00686272v4⟩



Record views


Files downloads