ON THE CAUCHY PROBLEM FOR BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN HOLDER SPACES

• 成果类型: Article
• 署名作者: Tang, Shanjian; Wei, Wenning
• 署名单位: Fudan University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP976
• 发表日期: 2016
• 页码: 360-398
• 关键词: maximum principle; adapted solution; Duality

摘要

This paper is concerned with solution in Holder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic spatial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional Holder spaces for them and give some inequalities among these Holder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.