Exponential ergodicity of Lévy driven Langevin dynamics with singular potentials

In this paper, we address exponential ergodicity for Lévy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of N particles moving in Rd and subject to discontinuous stochastic forces. In particular, our results are appli...

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Bibliographic Details
Published in:Stochastic processes and their applications 2024-06, Vol.172, p.104341, Article 104341
Main Authors: Bao, Jianhai, Fang, Rongjuan, Wang, Jian
Format: Article
Language:English
Subjects:
Exponential ergodicity
Langevin dynamic
Lyapunov function
Lévy noise
Singular potential
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Summary:In this paper, we address exponential ergodicity for Lévy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of N particles moving in Rd and subject to discontinuous stochastic forces. In particular, our results are applicable to the singular setups concerned with not only the Lennard-Jones-like interaction potentials but also the Coulomb potentials. In addition to Harris’ theorem, the approach is based on novel constructions of proper Lyapunov functions (which are completely different from the setting for Langevin dynamics driven by Brownian motions), on invoking the Hörmander theorem for non-local operators and on solving the issue on an approximate controllability of the associated deterministic system as well as on exploiting the time-change idea.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2024.104341