APPROXIMATION AND SUPPORT THEOREM IN HOLDER NORM FOR PARABOLIC STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: BALLY, V; MILLET, A; SANZSOLE, M
• 署名单位: Sorbonne Universite; University of Barcelona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988383
• 发表日期: 1995
• 页码: 178-222
• 关键词: diffusion

摘要

The solution u(t, x) of a parabolic stochastic partial differential equation is a random element of the space C-alpha,C-beta of Holder continuous functions on [0, T] x [0, 1] of order (alpha = 1/4 - epsilon in the time variable and beta = 1/2 - epsilon in the space variable, for any epsilon > 0. We prove a support theorem in C-alpha,C-beta for the law of u. The proof is based on an approximation procedure in Holder norm (which should have its own interest) using a space-time polygonal interpolation for the Brownian sheet driving the SPDE, and a sequence of absolutely continuous transformations of the Wiener space.