Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging

Abstract

Our first result is a stochastic sewing lemma with quantitative estimates for mild incremental processes, with which we study SPDEs driven by fractional Brownian motions in a random environment. We obtain uniform $L^p$-bounds. Our second result is a fractional averaging principle admitting non-stationary fast environments. As an application, we prove a fractional averaging principle for SPDEs.

arXiv commentTo appear in Stochastics and Dynamics; 38 pages

References in corpus (10)

• Analysis of the Rosenblatt process
• Rough evolution equations
• Averaging dynamics driven by fractional Brownian motion
• Taylor expansions of solutions of stochastic partial differential equations with additive noise
• Generalised Fractional Evolution Equations of Caputo Type
• Functional limit theorems for the fractional Ornstein-Uhlenbeck process
• Sample Paths Estimates for Stochastic Fast-Slow Systems driven by Fractional Brownian Motion
• Functional Limit Theorems for Volterra Processes and Applications to Homogenization
• Diffusive and rough homogenisation in fractional noise field
• Stochastic sewing in Banach space

Cited by in corpus (2)

• Generating diffusions with fractional Brownian motion
• Optimal rate of convergence for approximations of SPDEs with non-regular drift