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One-dimensional Brownian motion and the three-dimensional Bessel process

Published online by Cambridge University Press:  01 July 2016

James W. Pitman
James W. Pitman*
Affiliation:
University of Copenhagen∗
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Abstract

A simple path transformation is described which connects one-dimensional Brownian motion with the radial part of three-dimensional Brownian motion. This provides simple proofs of various path decompositions for these processes described by David Williams.

Keywords

BROWNIAN MOTIONBESSEL PROCESSPATH DECOMPOSITIONWEAK CONVERGENCE OF RANDOM WALKS TO DIFFUSIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 511 - 526
Copyright
Copyright © Applied Probability Trust 1975 

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