On uniqueness of maximal coupling for diffusion processes with a reflection

Kazumasa Kuwada

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 languageEnglish
Pages (from-to)935-957
Number of pages23
JournalJournal of Theoretical Probability
Issue number4
Publication statusPublished - 2007 Dec
Externally publishedYes


  • 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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