Almost automorphic solutions for stochastic differential equations driven by Levy noise with exponential dichotomy

被引：7
作者：
Sun, Kai [1 ]
Wang, Yan [2 ]
机构：
[1] Jilin Univ, Sch Math, 2699 Qianjin St, Changchun 130012, Jilin Province, Peoples R China
[2] Dalian Univ Technol, Sch Math Sci, Dalian, Peoples R China
来源：
STOCHASTIC ANALYSIS AND APPLICATIONS | 2017年 / 35卷 / 02期
关键词：
Almost automorphic solution; stochastic differential equation; exponential dichotomy; Levy process; ALMOST-PERIODIC SOLUTIONS; EXISTENCE;
D O I：
10.1080/07362994.2016.1237878
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we study almost automorphic solutions for semilinear stochastic differential equations driven by Levy noise. We establish the existence and uniqueness of bounded solutions by using the Banach fixed point theorem, the exponential dichotomy property and stochastic analysis techniques. Furthermore, this unique bounded solution is almost automorphic in distribution under slightly stronger conditions. We also give two examples to illustrate our results.
引用
收藏
页码：211 / 236
页数：26
相关论文
共 31 条
[1]  
Acquistapace P., 1987, Rend. Semin. Mat. Univ. Padova, V78, P47, DOI [10.1016/0022-1236(85)90050-3, DOI 10.1016/0022-1236(85)90050-3]
[2]  
[Anonymous], 2003, Real Analysis and Probability
[3]  
[Anonymous], 1974, Almost Periodic Differential Equations
[4]  
[Anonymous], 2013, Cambridge Studies in Advanced Mathematics
[5]  
Applebaum D., 2009, LEVY PROCESS STOCHAS, DOI [10.1017/CBO9780511809781, DOI 10.1017/CBO9780511809781]
[6]  
Arnold L., 1998, Stochastics Stochastics Rep., V64, P177
[7]  
Bezandry P., 2007, Electr. J. Diff. Equ, V117, P1
[8]   Existence of almost periodic solutions to some stochastic differential equations [J].
Bezandry, Paul H. ;
Diagana, Toka .
APPLICABLE ANALYSIS, 2007, 86 (07) :819-827
[9]  
Bezandry PH, 2011, ALMOST PERIODIC STOCHASTIC PROCESSES, P1, DOI 10.1007/978-1-4419-9476-9
[10]  
Bochner S., 1955, Univ. e Politec. Torino. Rend. Sem. Mat, V15, P225
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