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arXiv · 2108.05573

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

Xue-Mei Li·Julian Sieber
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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.

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Xue-Mei Li, Julian Sieber. 2021-08-12. Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging. https://doi.org/10.1142/s0219493722400251

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