On the small time asymptotics of diffusion processes on Hilbert spaces

• 成果类型: Article
• 署名作者: Zhang, TS
• 署名单位: University of Manchester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160252
• 发表日期: 2000
• 页码: 537-557
• 关键词: generalized schrodinger-operators; uniqueness; EQUATIONS

摘要

In this paper, we establish a small time large deviation principle and obtain the following small time asymptotics: lim(t-->0) 2t log P(X-0 is an element of B, X-t is an element of C) = -d(2)(B, C), for diffusion processes on Hilbert spaces, where d(B, C) is the intrinsic metric between two subsets B and C associated with the diffusions. The case of perturbed Ornstein-Uhlenbeck processes is treated separately at the end of the paper.