Kazumasa Kuwada
Published 2007-01-13Version 1
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.
Excursions of diffusion processes and continued fractions
On diffusion processes with drift in $L_{d+1}$
Fractional smoothness of functionals of diffusion processes under a change of measure
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