Optimal regularity of stochastic evolution equations in M-type 2 Banach spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Hong, Jialin^1,2  Huang, Chuying^1,2  Liu, Zhihui³ 

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

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

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

关键词: Stochastic evolution equation;    Multiplicative noise;    Well-posedness;    Trajectory regularity;    Factorization method;   

DOI  :  10.1016/j.jde.2019.03.003

来源: Elsevier

【 摘 要 】

In this paper, we prove the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces. The main idea of our method is to combine the approach in [9] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space. Applying our main results to the stochastic heat equation gives a positive answer to an open problem proposed in [10]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free