论文标题
路径独特的解决方案和随机平均，用于由布朗运动和布朗运动驱动的混合随机部分微分方程
Pathwise unique solutions and stochastic averaging for mixed stochastic partial differential equations driven by fractional Brownian motion and Brownian motion
论文作者
论文摘要
本文专门针对一个随机部分微分方程（SPDE）的系统，该系统具有由小数布朗运动（FBM）驱动的缓慢组分，其中hurst参数$ h> 1/2 $以及由快速变化扩散驱动的快速组件。它在两个方面改善了以前的工作：首先，使用停止时间技术和FBM的近似值，我们证明了由FBM和Brownian Motion驱动的一类混合SPDE的存在和独特定理。其次，建立了由FBM驱动的SPDE的平均原理，但要经受额外的快速扩散过程。为了进行这些改进，我们将基于广义的Stieltjes集成理论与ITôStochasticconculus相结合。然后，我们获得了慢组分的所需极限过程，该过程强烈依赖于快速变化的扩散过程的不变度量。
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.
