Invariant measures for stochastic functional differential equations

被引:26
作者
Butkovsky, Oleg [1 ,2 ]
Scheutzow, Michael [2 ]
机构
[1] Technion Israel Inst Technol, Fac Ind Engn & Management, IL-3200003 Haifa, Israel
[2] Tech Univ Berlin, Inst Math, Fak 2, MA 7-5,Str 17 Juni 136, D-10623 Berlin, Germany
来源
ELECTRONIC JOURNAL OF PROBABILITY | 2017年 / 22卷
基金
以色列科学基金会; 美国国家科学基金会;
关键词
stochastic functional differential equations; invariant measure; Lyapunov function; Veretennikov-Khasminskii condition; MARKOV-PROCESSES; SUBGEOMETRIC RATES; CONVERGENCE; DRIVEN; SDES;
D O I
10.1214/17-EJP122
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and exponential or subexponential convergence to the equilibrium. The obtained conditions extend the Veretennikov-Khasminskii conditions for SDEs and are optimal in a certain sense.
引用
收藏
页数:23
相关论文
共 27 条
[1]   Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincare [J].
Bakry, Dorninique ;
Cattiaux, Patrick ;
Guillin, Arnaud .
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (03) :727-759
[2]   The Monge-Kantorovich problem: achievements, connections, and perspectives [J].
Bogachev, V. I. ;
Kolesnikov, A. V. .
RUSSIAN MATHEMATICAL SURVEYS, 2012, 67 (05) :785-890
[3]   SUBGEOMETRIC RATES OF CONVERGENCE OF MARKOV PROCESSES IN THE WASSERSTEIN METRIC [J].
Butkovsky, Oleg .
ANNALS OF APPLIED PROBABILITY, 2014, 24 (02) :526-552
[4]   Subgeometric rates of convergence of f-ergodic strong Markov processes [J].
Douc, Randal ;
Fort, Gersende ;
Guillin, Arnaud .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (03) :897-923
[5]   HARNACK INEQUALITY FOR FUNCTIONAL SDEs WITH BOUNDED MEMORY [J].
Es-Sarhir, Abdelhadi ;
Von Renesse, Max-K. ;
Scheutzow, Michael .
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2009, 14 :560-565
[6]  
Gusak D., 2010, THEORY STOCHASTIC PR
[7]   On stationary solutions of delay differential equations driven by a Levy process [J].
Gushchin, AA ;
Küchler, U .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2000, 88 (02) :195-211
[8]   Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations [J].
Hairer, M. ;
Mattingly, J. C. ;
Scheutzow, M. .
PROBABILITY THEORY AND RELATED FIELDS, 2011, 149 (1-2) :223-259
[9]  
Hairer M., 2010, Convergence of Markov processes
[10]  
Hairer M, 2011, PROG PROBAB, V63, P109