Characterization of maximal Markovian couplings for diffusion processes

Kazumasa Kuwada

doi:10.1214/EJP.v14-634

Characterization of maximal Markovian couplings for diffusion processes

Kazumasa Kuwada

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

7 Citations (Scopus)

Abstract

Necessary conditions for the existence of a maximal Markovian coupling of diffusion processes are studied. A sufficient condition described as a global symmetry of the processes is revealed to be necessary for the Brownian motion on a Riemannian homogeneous space. As a result, we find many examples of a diffusion process which admits no maximal Markovian coupling. As an application, we find a Markov chain which admits no maximal Markovian coupling for specified starting points.

Original language	English
Pages (from-to)	633-662
Number of pages	30
Journal	Electronic Journal of Probability
Volume	14
DOIs	https://doi.org/10.1214/EJP.v14-634
Publication status	Published - 2009 Jan 1
Externally published	Yes

Keywords

Diffusion process
Markov chain
Markovian coupling
Maximal coupling

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/EJP.v14-634

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abstract = "Necessary conditions for the existence of a maximal Markovian coupling of diffusion processes are studied. A sufficient condition described as a global symmetry of the processes is revealed to be necessary for the Brownian motion on a Riemannian homogeneous space. As a result, we find many examples of a diffusion process which admits no maximal Markovian coupling. As an application, we find a Markov chain which admits no maximal Markovian coupling for specified starting points.",

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AB - Necessary conditions for the existence of a maximal Markovian coupling of diffusion processes are studied. A sufficient condition described as a global symmetry of the processes is revealed to be necessary for the Brownian motion on a Riemannian homogeneous space. As a result, we find many examples of a diffusion process which admits no maximal Markovian coupling. As an application, we find a Markov chain which admits no maximal Markovian coupling for specified starting points.

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Characterization of maximal Markovian couplings for diffusion processes

Abstract

Keywords

ASJC Scopus subject areas

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