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.
Original language | English |
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Pages (from-to) | 935-957 |
Number of pages | 23 |
Journal | Journal of Theoretical Probability |
Volume | 20 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2007 Dec |
Externally published | Yes |
Keywords
- Diffusion process
- Kendall-Cranston coupling
- Maximal coupling
- Mirror coupling
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty