Abstract
We consider a Wong–Zakai process, which is the difference of a Wiener-like process. We then prove that there are random attractors for non-autonomous Ginzburg–Landau equations driven by linear multiplicative noise in terms of Wong–Zakai process and Wiener-like process, respectively. Moreover, we establish the upper semi-continuity of random attractors as the size of difference noise tends to zero.
Highlights
Given a Wiener process, its δ-difference is called a Wong–Zakai process [40, 41]
On the probability space (Ω, F, P), we obtain a stochastic process given by W (t, ω) = ω(t), which is called a Wiener-like process [21]
Lu and Wang [27] have studied both the existence and approximation of random attractors for the reaction–diffusion equation driven by difference noise of a Wiener process
Summary
Given a Wiener process, its δ-difference is called a Wong–Zakai process [40, 41]. Such difference noise was often used to study stochastic equations as an approximation of white noise [15, 17, 19, 28, 30, 31]. On the probability space (Ω, F , P), we obtain a stochastic process given by W (t, ω) = ω(t), which is called a Wiener-like process [21]. A Wiener-like process only satisfies the properties on the right-hand side of (1.1). We do not require other properties (such as increment independence and Gauss distribution) of a Wiener process
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
