Large deviation for stochastic line integrals as L p -currents
成果类型：
Article
署名作者：
Kusuoka, Shigeo; Kuwada, Kazumasa; Tamura, Yozo
署名单位：
Ochanomizu University; University of Tokyo; Keio University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-009-0219-5
发表日期：
2010
页码：
649-674
关键词：
摘要：
The large deviation principle for stochastic line integrals along Brownian paths on a compact Riemannian manifold is studied. We regard them as a random map on a Sobolev space of 1-forms. We show that the differentiability order of the Sobolev space can be chosen to be almost independent of the dimension of the underlying space by assigning higher integrability on 1-forms. The large deviation is formulated for the joint distribution of stochastic line integrals and the empirical distribution of a Brownian path. As the result, the rate function is given explicitly.