Quantitative ergodicity for some switched dynamical systems

By M. Benaim, St'ephane Le Borgne, Florent Malrieu, Pierre-André Zitt. 2012

86 citations recorded by the source corpus.

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.

Subfields: Finance, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f9c4965fad73242edaeb2657380daa92543ba3de

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Citations in the corpus

Criteria for transience and recurrence of regime-switching diffusion processes * (2014, background): “his complicatedness, it is a challenging work to determine the recurrent property of a regime-switching diﬀusion process. There are lots of work having been dedicated to this task. See, for instance, [1, 3, 5, 11, 12, 16] and references therein. Besides constructing the examples we mentioned above, ”
Qualitative properties of certain piecewise deterministic Markov processes (2012, background): “Under more stringent assumptions, [4] gives an explicit rate of convergence in Wasserstein distance, via a coupling argument.”
Sensitivity to switching rates in stochastically switched odes (2013, background): “[6], [3], [4], and [1] all study invariant measures for such processes.”