Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations
发表时间：2020-06-09
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- 论文类型：
- 期刊论文
- 第一作者：
- Cheban, David
- 通讯作者：
- Liu, ZX (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
- 合写作者：
- Liu, Zhenxin
- 发表时间：
- 2020-08-05
- 发表刊物：
- JOURNAL OF DIFFERENTIAL EQUATIONS
- 收录刊物：
- SCIE
- 文献类型：
- J
- 卷号：
- 269
- 期号：
- 4
- 页面范围：
- 3652-3685
- ISSN号：
- 0022-0396
- 关键字：
- Stochastic differential equation; Quasi-periodic solution; Bohr/Levitan almost periodic solution; Almost automorphic solution; Birkhoff recurrent solution; Poisson stable solution; Asymptotic stability
- 摘要：
- The paper is dedicated to studying the problem of Poisson stability (in particular stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in the sense of Bebutov, Levitan almost periodicity, pseudo-periodicity, pseudo-recurrence, Poisson stability) of solutions for semi-linear stochastic equation dx(t) = (Ax(t) + f(t, x(t)))dt + g(t, x(t))dW(t) (*) with exponentially stable linear operator A and Poisson stable in time coefficients f and g. We prove that if the functions f and g are appropriately "small", then equation (*) admits at least one solution which has the same character of recurrence as the functions f and g. We also discuss the asymptotic stability of these Poisson stable solutions. (C) 2020 Elsevier Inc. All rights reserved.
- 是否译文：
- 否
