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Stochastic Volterra equations in Banach spaces and stochastic partial differential equation. (English) Zbl 1189.60124

Author’s abstract: We study the existence-uniqueness and large deviation estimate for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then we apply them to a large class of semilinear stochastic partial differential equations (SPDE), and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Moreover, stochastic Navier-Stokes equations are also investigated.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60B11 Probability theory on linear topological spaces
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