Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

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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. © 2009 Elsevier Inc. All rights reserved.

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APA

Zhang, X. (2010). Stochastic Volterra equations in Banach spaces and stochastic partial differential equation. Journal of Functional Analysis, 258(4), 1361–1425. https://doi.org/10.1016/j.jfa.2009.11.006

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