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On the Duality between Coalescing Brownian Motions

Published online by Cambridge University Press:  20 November 2018

Jie Xiong  and
Xiaowen Zhou
Jie Xiong
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1 and Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 U.S.A.
Xiaowen Zhou
Affiliation:
Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, H4B 1R6 e-mail: xzhou@mathstat.concordia.ca
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Abstract

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A duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.

Keywords

60J6560G57coalescing Brownian motionsdualitymartingale problemmeasure-valued processes
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 1 , 01 February 2005 , pp. 204 - 224
Copyright
Copyright © Canadian Mathematical Society 2005

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