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arXiv · 1011.2615

Infinitely delayed stochastic evolution equations in UMD Banach spaces

Paul Crewe
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Abstract

We prove an existence and uniqueness result for the infinitely delayed stochastic evolution equation $$dU(t) = &\big(AU(t) + F(t,U_t)\big) dt + B(t,U_t)dW_H(t), t\in[0,T_0]$$ where $A$ is the generator of an analytic semigroup on a UMD space $E$, $F$ and $B$ satisfy Lipschitz conditions and $\mathscr{B}$ is a weighted $L^p$ history space. This paper is based on recent work of van Neerven \emph{et al.}~which developed the theory of abstract stochastic evolution equations in UMD spaces.

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Paul Crewe. 2010-11-11. Infinitely delayed stochastic evolution equations in UMD Banach spaces. https://arxiv.org/abs/1011.2615

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