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      Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise

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          Abstract

          We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic character. Under appropriate Lipschitz-type and linear growth assumptions on the nonlinear terms we show that the unique mild solution is mean-\(p\) H\"older continuous with values in an appropriate Sobolev space depending on the kernel and the data. In particular, we obtain pathwise space-time (Sobolev-H\"older) regularity of the solution together with a maximal type bound on the spatial Sobolev norm. As one of the main technical tools we establish a smoothing property of the derivative of the deterministic evolution operator family.

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          On the discretization in time of parabolic stochastic partial differential equations

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            Error Estimates with Smooth and Nonsmooth Data for a Finite Element Method for the Cahn-Hilliard Equation

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              Existence and asymptotic behavior for hereditary stochastic evolution equations

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                Author and article information

                Journal
                2014-04-15
                2014-05-14
                Article
                10.1016/j.jde.2014.09.020
                1404.4131
                5b99bcd6-9e05-4473-86da-6c5fa3730ab0

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                J. Diff. Eq., 258(2) (2015), 535-554
                math.PR

                Probability
                Probability

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