Characterization of maximal Markovian couplings for diffusion processes
Kazumasa Kuwada, Ochanomizu University
Abstract
Necessary conditions for the existence of a maximal Markovian coupling of diffu-
sion 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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