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 |
|---|---|
| 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 1 |
Keywords
- Diffusion process
- Kendall-Cranston coupling
- Maximal coupling
- Mirror coupling
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty
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Kuwada, K. (2007). On uniqueness of maximal coupling for diffusion processes with a reflection. Journal of Theoretical Probability, 20(4), 935-957. https://doi.org/10.1007/s10959-007-0087-9