Electron. J. Differential Equations, Vol. 2020 (2020), No. 113, pp. 1-9.

Continuous dependence of recurrent solutions for stochastic differential equations

Haijing Qiu, Yan Wang

Abstract:
Existence, uniqueness and asymptotic stability of recurrent solutions have been investigated extensively for semi-linear stochastic differential equations. In this article, we show that the unique recurrent solution depends continuously on the coefficients of the equation in the compact-open topology or uniform topology, which depends on how the coefficients vary with respect to the parameter.

Submitted August 2, 2020. Published November 17, 2020.
Math Subject Classifications: 35B30, 37L15, 37B20, 60H10.
Key Words: Stochastic differential equation; continuous dependence; recurrent solution.
DOI: 10.58997/ejde.2020.113

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Haijing Qiu
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: 18233150561@163.com
Yan Wang
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: wangyan84@dlut.edu.cn

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