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abstract: 'This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst parameter $H >1/2$ and a fast component driven by fast-varying diffusion. It improves previous work in two aspects: Firstly, using a stopping time technique and an approximation of the fBm, we prove an existence and uniqueness theorem for a class of mixed SPDEs driven by both fBm and Brownian motion; Secondly, an averaging principle in the mean square sense for SPDEs driven by fBm subject to an additional fast-varying diffusion process is established. To carry out these improvements, we combine the pathwise approach based on the generalized Stieltjes integration theory with the Itô stochastic calculus. Then, we obtain a desired limit process of the slow component which strongly relies on an invariant measure of the fast-varying diffusion process.'
address:
- 'School of Mathematical Sciences, Fudan University, Shanghai, 200433, China and Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan'
- 'Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan'
- 'School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, China'
author:
- Bin PEI
- Yuzuru INAHAMA
- Yong XU
