Convergence of <i>p</i>-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion

Abstract

In this paper, we focus on fast-slow stochastic partial differential equations in which the slow variable is driven by a fractional Brownian motion and the fast variable is driven by an additive Brownian motion. We establish an averaging principle in which the fast-varying diffusion process will be averaged out with respect to its stationary measure in the limit process. It is shown that the slow-varying process \begin{document}$ L^{p}(p \geq 2) $\end{document} converges to the solution of the corresponding averaging equation. To reduce the complexity, one can concentrate on the limit process instead of studying the original full fast-slow system.