Strong existence and uniqueness to a class of nonlinear SPDEs driven by Gaussian colored noises

Jie Xiong and Xu Yang

Statistics & Probability Letters, 2017, vol. 129, issue C, 113-119

Abstract: In this paper, we establish the strong existence and uniqueness to the following stochastic partial differential equation: ut(x)=u0(x)+12∫0tΔus(x)ds+∫0t∫Rg(us(x),∇us(x))dF(s,y),where F(s,x) is a Gaussian noise on R+×R that is white in time and colored in space. This gives an affirmative answer to the open problem in Gomez et al. (2013) for certain non-Lipschitz condition of g.

Keywords: Stochastic partial differential equation; Existence; Uniqueness; Colored noise (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.05.012

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