Stochastic Volterra equations in Banach spaces and stochastic partial differential equation |
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| Authors: | Xicheng Zhang |
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| Affiliation: | a Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
b School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia |
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| Abstract: | In this paper, 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. |
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| Keywords: | Stochastic Volterra equation Large deviation Stochastic Navier-Stokes equation |
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