Stochastic evolution equations with random generators

• 成果类型: Article
• 署名作者: Leon, JA; Nualart, D
• 署名单位: Instituto Politecnico Nacional - Mexico; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; University of Barcelona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 149-186
• 关键词: calculus

摘要

We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the Wiener process. The proof is based on a maximal inequality for the Skorohod integral deduced from the Ito's formula for this anticipating stochastic integral.