THE RADIAL PART OF BROWNIAN-MOTION .2. ITS LIFE AND TIMES ON THE CUT LOCUS
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 0178-8051Full text not available from this repository.
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|
|Number of Pages:||16|
|Page Range:||pp. 353-368|
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