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

被引：3
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
相关论文
共 86 条
[11]  
BENAROUS G, 1994, ANN I H POINCARE-PR, V30, P415
[12]  
Bertoldi M., 2007, PURE APPL MATH
[13]   A generalized parallel replica dynamics [J].
Binder, Andrew ;
Lelievre, Tony ;
Simpson, Gideon .
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 284 :595-616
[14]  
Bogachev V. I., 2015, MATH SURVEYS MONOGRA, V207
[15]  
CATTIAUX P, 1991, B SCI MATH, V115, P81
[16]   Hitting times, functional inequalities, Lyapunov conditions and uniform ergodicity [J].
Cattiaux, Patrick ;
Guillin, Arnaud .
JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (06) :2361-2391
[17]   Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction [J].
Cattiaux, Patrick ;
Meleard, Sylvie .
JOURNAL OF MATHEMATICAL BIOLOGY, 2010, 60 (06) :797-829
[18]   QUASI-STATIONARY DISTRIBUTIONS AND DIFFUSION MODELS IN POPULATION DYNAMICS [J].
Cattiaux, Patrick ;
Collet, Pierre ;
Lambert, Amaury ;
Martinez, Servet ;
Meleard, Sylvie ;
San Martin, Jaime .
ANNALS OF PROBABILITY, 2009, 37 (05) :1926-1969
[19]   Lyapunov conditions for Super Poincare inequalities [J].
Cattiaux, Patrick ;
Guillin, Arnaud ;
Wang, Feng-Yu ;
Wu, Liming .
JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (06) :1821-1841
[20]   General criteria for the study of quasi-stationarity [J].
Champagnat, Nicolas ;
Villemonais, Denis .
ELECTRONIC JOURNAL OF PROBABILITY, 2023, 28
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