A counterexample for the optimality of Kendall-Cranston coupling

Kazumasa Kuwada (Ochanomizu University)
Karl-Theodor Sturm (Institute for applied mathematics, University of Bonn)

Abstract


We construct a Riemannian manifold where the Kendall-Cranston coupling of two Brownian particle does not maximize the coupling probability.

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Pages: 66-72

Publication Date: April 3, 2007

DOI: 10.1214/ECP.v12-1160

References

  1. M. Cranston. Gradient estimates on manifolds using coupling. J. Funct. Anal. 99 (1991), no. 1, 110--124. Math review 93a:58175
  2. E.-P. Hsu, K.-Th. Sturm. Maximal coupling of Euclidean Brownian motions. preprint.
  3. W. S. Kendall. Nonnegative Ricci curvature and the Brownian coupling property. Stochastics 19 (1986), no. 1-2, 111--129. Math Review 88e:60092
  4. K. Kuwada. On uniqueness of maximal coupling for diffusion processes with a reflection. to appear in Journal of Theoretical Probability.
  5. M.-K. von Renesse. Intrinsic coupling on Riemannian manifolds and polyhedra. Electron. J. Probab. 9 (2004), no. 14, 411--435. Math Review 2005i:60158
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