Abstract
In this paper, we investigate the exponential ergodicity in a Wasserstein-type distance for a damping Hamiltonian dynamics with state-dependent and non-local collisions, which indeed is a special case of piecewise deterministic Markov processes that is very popular in numerous modelling situations including stochastic algorithms. The approach adopted in this work is based on a combination of the refined basic coupling and the refined reflection coupling for non-local operators. In a certain sense, the main result developed in the present paper is a continuation of the counterpart in (Stochastic Process. Appl. (2022) 146 114–142) on exponential ergodicity of stochastic Hamiltonian systems with Lévy noises and a complement of (Ann. Inst. Henri Poincaré Probab. Stat. 58 (2022a) 916–944) upon exponential ergodicity for Andersen dynamics with constant jump rate functions.
Funding Statement
The first author was supported by NSF of China (Nos. 12071340 and 11831014). The second author was supported in part by of China (Nos. 11831014, 12071076 and 12225104), and the Education and Research Support Program for Fujian Provincial Agencies.
Acknowledgements
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Citation
Jianhai Bao. Jian Wang. "Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions." Bernoulli 29 (3) 2442 - 2465, August 2023. https://doi.org/10.3150/22-BEJ1548
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