On uniqueness of maximal coupling for diffusion processes with a reflection

Details On uniqueness of maximal coupling for diffusion processes with a reflection On uniqueness of maximal coupling for diffusion processes with a reflection

2007-01-13

arxiv.org/abs/math/0701372v1

Mathematics

Probability

23 pages

Scientific paper

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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