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Stochastic maximal $L^p$-regularity

Veraar, M (TUDelft)
Friday 08 January 2010, 14:00-15:00

Seminar Room 1, Newton Institute


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 \[\int_0^t S(t-s) f(s) d W(s)\] satisfy optimal $L^p$-regularity estimates and maximal estimates. Here $S$ is an analytic semigroup on an $L^q$-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 $L^p$-regularity results from the literature. In particular, our framework covers and extends the important results of Krylov for the heat semigroup on $\mathbb{R}^d$.


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