Uniform Wasserstein convergence of penalized Markov processes

Nicolas Champagnat; Edouard Strickler; Denis Villemonais

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arXiv · 2306.16051

Uniform Wasserstein convergence of penalized Markov processes

Nicolas Champagnat·Edouard Strickler·Denis Villemonais

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Abstract

For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of application where our criterion can be checked, including Bernoulli convolutions and piecewise deterministic Markov processes of the form of switched dynamical systems, for which convergence in total variation is not possible.

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Nicolas Champagnat, Edouard Strickler, Denis Villemonais. 2023-06-28. Uniform Wasserstein convergence of penalized Markov processes. https://arxiv.org/abs/2306.16051

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