Ergodic theory for sdes with extrinsic memory

被引:44
作者
Hairer, M. [1 ]
Ohashi, A.
机构
[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England
[2] Univ Estadual Campinas, Dept Matemat, BR-13083970 Campinas, SP, Brazil
基金
英国工程与自然科学研究理事会;
关键词
non-Markovian processes; ergodicity; fractional Brownian motion;
D O I
10.1214/009117906000001141
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 develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas'minskii theorem. The second part of this article shows how it is possible to apply these results to the case of stochastic differential equations driven by fractional Brownian motion. It follows that under a nondegeneracy condition on the noise, such equations admit a unique adapted stationary solution.
引用
收藏
页码:1950 / 1977
页数:28
相关论文
共 22 条
[11]   Large deviations and support theorem for diffusion processes via rough paths [J].
Ledoux, M ;
Qian, Z ;
Zhang, T .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 102 (02) :265-283
[12]   Differential equations driven by rough signals [J].
Lyons, TJ .
REVISTA MATEMATICA IBEROAMERICANA, 1998, 14 (02) :215-310
[13]   FRACTIONAL BROWNIAN MOTIONS FRACTIONAL NOISES AND APPLICATIONS [J].
MANDELBROT, BB ;
VANNESS, JW .
SIAM REVIEW, 1968, 10 (04) :422-+
[14]  
Meyn S. P., 1994, MARKOV CHAINS STOCHA
[15]  
Nualart D., 2002, COLLECT MATH, V53, P55
[16]  
NUALART D, 2005, MALLIAVIN CALCULUS S
[17]  
Nualart D., 1996, MALLIAVIN CALCULUS R, V71, P168
[18]  
RUSSO F, 2000, STOCHASTICS STOCHAST, V70, P1
[19]   Stieltjes integrals of Holder continuous functions with applications to fractional Brownian motion [J].
Ruzmaikina, AA .
JOURNAL OF STATISTICAL PHYSICS, 2000, 100 (5-6) :1049-1069
[20]  
Samko SG., 1993, Fractional Integral and Derivatives: Theory and Applications