Infinitely delayed stochastic evolution equations in UMD Banach spaces

2010/11/11 by Paul Crewe, Crewe, Paul
Mathematics · #34K50 #35R60 #46N30 #47D06 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.AP #math.FA #math.PR #msc:34K50 #msc:35R60 #msc:46N30 #msc:47D06 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1011.2615

arxiv created 2010/11/11 · arxiv updated 2010/11/12

Abstract

We prove an existence and uniqueness result for the infinitely delayed stochastic evolution equation dU(t) = (AU(t) + F(t,U_t)) dt + B(t,U_t)dW_H(t), t∈[0,T₀] where A is the generator of an analytic semigroup on a UMD space E, F and B satisfy Lipschitz conditions and \mathscrB is a weighted L^p history space. This paper is based on recent work of van Neerven et al.~which developed the theory of abstract stochastic evolution equations in UMD spaces.

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