Stability properties of stochastic maximal L^p-regularity

2019/01/24 by Agresti, Antonio, Veraar, Mark · 1 citation
#42B37 #47D06 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 60H15 #Probability (math.PR) #Secondary: 35B65

paper · doi:10.48550/arxiv.1901.08408

Abstract

In this paper we consider L^p-regularity estimates for solutions to stochastic evolution equations, which is called stochastic maximal L^p-regularity. Our aim is to find a theory which is analogously to Dore's theory for deterministic evolution equations. He has shown that maximal L^p-regularity is independent of the length of the time interval, implies analyticity and exponential stability of the semigroup, is stable under perturbation and many more properties. We show that the stochastic versions of these results hold.

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• A stochastic flow approach to De Giorgi-Nash-Moser estimates for SPDEs with smooth transport noise

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