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Stochastic maximal $L^p$-regularity

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Stochastic Partial Differential Equations

In this talk we discuss our recent progress on maximal regularity of convolutions with respect to Brownian motion. Under certain conditions, we show that stochastic convolutions [int_0t S(t-s) f(s) d W(s)] satisfy optimal $Lp$-regularity estimates and maximal estimates. Here $S$ is an analytic semigroup on an $Lq$-space. We also provide counterexamples to certain limiting cases and explain the applications to stochastic evolution equations. The results extend and unifies various known maximal $Lp$-regularity results from the literature. In particular, our framework covers and extends the important results of Krylov for the heat semigroup on $mathbb{R}^d$.

This talk is part of the Isaac Newton Institute Seminar Series series.

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