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On Uniqueness of Maximal Coupling for Diffusion Processes with a Reflection

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ochanomizu University, Tokyo, 112-8610, Japan

    Kazumasa Kuwada

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  1. Kazumasa Kuwada
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Correspondence to Kazumasa Kuwada.

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Kuwada, K. On Uniqueness of Maximal Coupling for Diffusion Processes with a Reflection. J Theor Probab 20, 935–957 (2007). https://doi.org/10.1007/s10959-007-0087-9

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  • DOI: https://doi.org/10.1007/s10959-007-0087-9

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