On uniqueness of maximal coupling for diffusion processes with a reflection

Kazumasa Kuwada

doi:10.1007/s10959-007-0087-9

On uniqueness of maximal coupling for diffusion processes with a reflection

Kazumasa Kuwada

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

A maximal coupling of two diffusion processes makes two diffusion particles meet as early as possible. We study the uniqueness of maximal couplings under a sort of 'reflection structure' which ensures the existence of such couplings. In this framework, the uniqueness in the class of Markovian couplings holds for the Brownian motion on a Riemannian manifold whereas it fails in more singular cases. We also prove that a Kendall-Cranston coupling is maximal under the reflection structure.

Original language	English
Pages (from-to)	935-957
Number of pages	23
Journal	Journal of Theoretical Probability
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s10959-007-0087-9
Publication status	Published - 2007 Dec
Externally published	Yes

Keywords

Diffusion process
Kendall-Cranston coupling
Maximal coupling
Mirror coupling

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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10.1007/s10959-007-0087-9

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AB - A maximal coupling of two diffusion processes makes two diffusion particles meet as early as possible. We study the uniqueness of maximal couplings under a sort of 'reflection structure' which ensures the existence of such couplings. In this framework, the uniqueness in the class of Markovian couplings holds for the Brownian motion on a Riemannian manifold whereas it fails in more singular cases. We also prove that a Kendall-Cranston coupling is maximal under the reflection structure.

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KW - Kendall-Cranston coupling

KW - Maximal coupling

KW - Mirror coupling

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On uniqueness of maximal coupling for diffusion processes with a reflection

Abstract

Keywords

ASJC Scopus subject areas

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