Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems

被引：2
作者：
Guillin, Arnaud [1 ]
Nectoux, Boris [1 ]
Wu, Liming [2 ]
机构：
[1] Univ Clermont Auvergne, Lab Math, F-63178 Aubiere, France
[2] Univ Blaise Pascal, Lab Math Appl, CNRS UMR 6620, F-63177 Aubiere, France
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2024年 / 26卷 / 08期
关键词：
quasi-stationary distributions; Langevin process; Hamiltonian dynamics; metastability; molecular dynamics; ONE-DIMENSIONAL DIFFUSIONS; GENERAL STATE-SPACE; EXPONENTIAL CONVERGENCE; R-THEORY; DYNAMICS; CHAINS; ERGODICITY; TIME; APPROXIMATION; ASYMPTOTICS;
D O I：
10.4171/JEMS/1418
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a general result on the existence and uniqueness of a quasi-stationary distribution mu (D) of a strongly Feller Markov process ( X-t , t > 0) killed when it exits a domain D, under some Lyapunov function condition. Our result covers the case of hypoelliptic damped Hamiltonian systems. Our method is based on a characterization of the essential spectral radius by means of Lyapunov functions and measures of noncompactness.
引用
收藏
页码：3047 / 3090
页数：44
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