Uniform Wasserstein convergence of penalized Markov processes

• 成果类型: Article
• 署名作者: Champagnat, Nicolas; Strickler, Edouard; Villemonais, Denis
• 署名单位: Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Inria; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01385-6
• 发表日期: 2025
• 页码: 1031-1069
• 关键词: quasi-stationary distributions; distance

摘要

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.