On the sample paths of Brownian motions on compact infinite dimensional groups

• 成果类型: Article
• 署名作者: Bendikov, A; Saloff-Coste, L
• 署名单位: Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 1464-1493
• 关键词: absolute continuity; semigroups; PRODUCTS

摘要

We study the regularity of the sample paths of certain Brownian motions on the infinite dimensional torus T-infinity and other compact connected groups in terms of the associated intrinsic distance. For each lambda is an element of (0, 1), we give examples where the intrinsic distance d is continuous and defines the topology of T-infinity and where the sample paths satisfy 0 < lim inf(t-->0) d(X-0,X-t)/t((1-lambda)/2) less than or equal to lim sup(t-->0) d(X-0,X-t)/t((1-lambda)/2) < infinity and [GRAPHICS]