Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

Xicheng Zhang

doi:10.1016/j.jfa.2009.11.006

Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

Xicheng Zhang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

77 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1361-1425
Number of pages	65
Journal	Journal of Functional Analysis
Volume	258
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2009.11.006
Publication status	Published - 15 Feb 2010
Externally published	Yes

Keywords

Large deviation
Stochastic Navier-Stokes equation
Stochastic Volterra equation

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10.1016/j.jfa.2009.11.006

Cite this

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title = "Stochastic Volterra equations in Banach spaces and stochastic partial differential equation",

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.",

keywords = "Large deviation, Stochastic Navier-Stokes equation, Stochastic Volterra equation",

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AB - 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.

KW - Large deviation

KW - Stochastic Navier-Stokes equation

KW - Stochastic Volterra equation

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U2 - 10.1016/j.jfa.2009.11.006

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M3 - Article

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JO - Journal of Functional Analysis

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IS - 4

ER -

Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

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Keywords

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