On the Cauchy problem for parabolic SPEDs in Holder classes

• 成果类型: Article
• 署名作者: Mikulevicius, R
• 署名单位: Vilnius University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 74-103
• 关键词: partial-differential equations

摘要

We study Cauchy's problem for certain second-order linear parabolic stochastic differential equation (SPDE) driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Holder classes.