Harnack inequality and derivative formula for SDE driven by fractional Brownian motion

被引：18
作者：
Fan XiLiang [1 ,2 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
[2] Anhui Normal Univ, Dept Math, Wuhu 241003, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Harnack inequality; stochastic differential equation; fractional Brownian motion; LOGARITHMIC SOBOLEV INEQUALITIES; DIFFERENTIAL-EQUATIONS; FUNCTIONAL INEQUALITIES; STOCHASTIC CALCULUS; TIME ASYMPTOTICS; RESPECT;
D O I：
10.1007/s11425-013-4569-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, Harnack inequality and derivative formula are established for stochastic differential equation driven by fractional Brownian motion with Hurst parameter H < 1/2. As applications, strong Feller property, log-Harnack inequality and entropy-cost inequality are given.
引用
收藏
页码：515 / 524
页数：10
相关论文
共 25 条
[1]   On the small time asymptotics of diffusion processes on path groups [J].
Aida, S ;
Zhang, T .
POTENTIAL ANALYSIS, 2002, 16 (01) :67-78
[2]  
Aida S, 2001, PROG PROBAB, V48, P77
[3]   Stochastic calculus with respect to Gaussian processes [J].
Alòs, E ;
Mazet, O ;
Nualart, D .
ANNALS OF PROBABILITY, 2001, 29 (02) :766-801
[4]  
[Anonymous], 1988, Special functions of mathematical physics
[5]   Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below [J].
Arnaudon, M ;
Thalmaier, A ;
Wang, FY .
BULLETIN DES SCIENCES MATHEMATIQUES, 2006, 130 (03) :223-233
[6]   Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds [J].
Arnaudon, Marc ;
Thalmaier, Anton ;
Wang, Feng-Yu .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (10) :3653-3670
[7]   Hypercontractivity of Hamilton-Jacobi equations [J].
Bobkov, SG ;
Gentil, I ;
Ledoux, M .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2001, 80 (07) :669-696
[8]   Stochastic analysis, rough path analysis and fractional Brownian motions [J].
Coutin, L ;
Qian, ZM .
PROBABILITY THEORY AND RELATED FIELDS, 2002, 122 (01) :108-140
[9]   Stochastic analysis of the fractional Brownian motion [J].
Decreusefond, L ;
Üstünel, AS .
POTENTIAL ANALYSIS, 1999, 10 (02) :177-214
[10]   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
123