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个人信息Personal Information
教授
博士生导师
硕士生导师
主要任职：数学科学学院院长、党委副书记
性别：男
毕业院校：吉林大学
学位：博士
所在单位：数学科学学院
学科：应用数学. 应用数学. 概率论与数理统计. 概率论与数理统计
办公地点：数学楼520室
联系方式：0411-84706570，0411-84708351-8520
电子邮箱：zxliu@dlut.edu.cn
Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations
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论文类型：期刊论文
发表时间：2020-08-05
发表刊物：JOURNAL OF DIFFERENTIAL EQUATIONS
收录刊物：SCIE
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.