Well-posedness and optimal regularity of stochastic evolution equations with multiplicative noises

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Hong, Jialin¹  Liu, Zhihui² 

[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China

[2] Hong Kong Univ Sci & Technol, Dept Math, Clear Water Bay, Hong Kong, Peoples R China

关键词: Stochastic evolution equation;    Multiplicative noise;    Trajectory regularity;    Factorization method;    Gronwall inequality with singular kernel;   

DOI  :  10.1016/j.jde.2018.10.005

来源: Elsevier

【 摘 要 】

In this paper, we establish the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the well-posedness of the problem, the linear operator of the equations is only need to be a generator of a C-0-semigroup and the proposed noises are quite general, which include space-time white noise and rougher noises. When the linear operator generates an analytic C-0-semigroup, we derive the optimal trajectory regularity of the solution through a generalized criterion of factorization method. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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