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THE RADIAL PART OF BROWNIAN-MOTION .2. ITS LIFE AND TIMES ON THE CUT LOCUS
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UNSPECIFIED (1993) THE RADIAL PART OF BROWNIAN-MOTION .2. ITS LIFE AND TIMES ON THE CUT LOCUS. PROBABILITY THEORY AND RELATED FIELDS, 96 (3). pp. 353-368. ISSN 0178-8051
Full text not available from this repository.Abstract
This paper is a sequel to Kendall (1987), which explained how the Ito formula for the radial part of Brownian motion X on a Riemannian manifold can be extended to hold for all time including those times at which X visits the cut locus. This extension consists of the subtraction of a correction term, a continuous predictable non-decreasing process L which changes only when X visits the cut locus. In this paper we derive a representation of L in terms of measures of local time of X on the cut locus. In analytic terms we compute an expression for the singular part of the Laplacian of the Riemannian distance function. The work uses a relationship of the Riemannian distance function to convexity, first described by Wu (1979) and applied to radial parts of GAMMA-martingales in Kendall (1993).
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Journal or Publication Title: | PROBABILITY THEORY AND RELATED FIELDS |
| Publisher: | SPRINGER VERLAG |
| ISSN: | 0178-8051 |
| Date: | August 1993 |
| Volume: | 96 |
| Number: | 3 |
| Number of Pages: | 16 |
| Page Range: | pp. 353-368 |
| Publication Status: | Published |
| URI: | http://wrap.warwick.ac.uk/id/eprint/21128 |
Data sourced from Thomson Reuters' Web of Knowledge
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