Nonlocal fractional stochastic differential equations driven by fractional Brownian motion

被引：5
作者：
Lv, Jingyun
Yang, Xiaoyuan [1 ,2 ]
机构：
[1] Beihang Univ, LMIB, Beijing 100191, Peoples R China
[2] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2017年
基金：
北京市自然科学基金; 中国国家自然科学基金;
关键词：
fractional stochastic differential equations; fractional Brownian motion; mild solution; nonlocal condition; DELAY EVOLUTION-EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; MILD SOLUTIONS; APPROXIMATE CONTROLLABILITY; EXISTENCE; IMPULSES;
D O I：
10.1186/s13662-017-1210-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a class of nonlocal fractional stochastic differential equations driven by fractional Brownian motion with Hurst index H > 1/2. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. Finally, an example is presented to illustrate our obtained results.
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页数：16
相关论文
共 25 条
[1]  
[Anonymous], 1998, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
[2]   Existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by a fractional Brownian motion [J].
Arthi, G. ;
Park, Ju H. ;
Jung, H. Y. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 32 :145-157
[3]   Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients [J].
Benchaabane, Abbes ;
Sakthivel, Rathinasamy .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 312 :65-73
[4]  
Biagini F, 2008, PROBAB APPL SER, P1
[5]   Existence of Mild Solutions to Stochastic Delay Evolution Equations with a Fractional Brownian Motion and Impulses [J].
Boudaoui, Ahmed ;
Caraballo, Tomas ;
Ouahab, Abdelghani .
STOCHASTIC ANALYSIS AND APPLICATIONS, 2015, 33 (02) :244-258
[6]   Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space [J].
Boufoussi, Brahim ;
Hajji, Salah .
STATISTICS & PROBABILITY LETTERS, 2012, 82 (08) :1549-1558
[7]   The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion [J].
Caraballo, T. ;
Garrido-Atienza, M. J. ;
Taniguchi, T. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) :3671-3684
[8]  
Christodoulou-Volos C., 2006, Applied Financial Economics, V16, P1331, DOI DOI 10.1080/09603100600829519
[9]   Nonlocal stochastic integro-differential equations driven by fractional Brownian motion [J].
Cui, Jing ;
Wang, Zhi .
ADVANCES IN DIFFERENCE EQUATIONS, 2016,
[10]   Existence result for fractional neutral stochastic integro-differential equations with infinite delay [J].
Cui, Jing ;
Yan, Litan .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (33)
123