THE INTRINSIC LOCAL TIME SHEET OF BROWNIAN-MOTION
成果类型：
Article
署名作者：
ROGERS, LCG; WALSH, JB
署名单位：
University of British Columbia
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/BF01418866
发表日期：
1991
页码：
363-379
关键词：
摘要：
McGill showed that the intrinsic local time process LBAR (t, x), t greater-than-or-equal-to 0, x-epsilon-IR, of one-dimensional Brownian motion is, for fixed t > 0, a supermartingale in the space variable, and derived an expression for its Doob-Meyer decomposition. This expression referred to the derivative of some process which was not obviously differentiable. In this paper, we provide an independent proof of the result, by analysing the local time of Brownian motion on a family of decreasing curves. The ideas involved are best understood in terms of stochastic area integrals with respect to the Brownian local time sheet, and we develop this approach in a companion paper. However, the result mentioned above admits a direct proof, which we give here; one is inevitably drawn to look at the local time process of a Dirichlet process which is not a semimartingale.
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