Stochastic Volterra equations in Banach spaces and stochastic partial differential equation
Copyright policy )Stochastic Volterra equations in Banach spaces and stochastic partial differential equation
In this paper, we first study the existence-uniqueness and large deviation estimate of solutions 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) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Lastly, high order SPDEs in a bounded domain of Euclidean space, second order SPDEs on complete Riemannian manifolds, as well as stochastic Navier-Stokes equations are investigated.
65Pages
- Huazhong University of Science and Technology China (People's Republic of)
- UNSW Sydney Australia
Stochastic Navier–Stokes equation, large deviation, Probability theory on linear topological spaces, Probability (math.PR), 60H15, 35R60, stochastic Navier-Stokes equation, Large deviation, Mathematics - Analysis of PDEs, Stochastic partial differential equations (aspects of stochastic analysis), FOS: Mathematics, stochastic Volterra equation, Stochastic Volterra equation, Analysis, Mathematics - Probability, Analysis of PDEs (math.AP)
Stochastic Navier–Stokes equation, large deviation, Probability theory on linear topological spaces, Probability (math.PR), 60H15, 35R60, stochastic Navier-Stokes equation, Large deviation, Mathematics - Analysis of PDEs, Stochastic partial differential equations (aspects of stochastic analysis), FOS: Mathematics, stochastic Volterra equation, Stochastic Volterra equation, Analysis, Mathematics - Probability, Analysis of PDEs (math.AP)
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