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Original Articles

The Expansion of Mean Distance of Brownian Motion on Riemannian Manifold

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Pages 169-191 | Published online: 16 Aug 2006

References

  • Gray , A. and Pinsky , M.A. 1983 . The mean exit time from a small geodesic ball in a Riemannian manifold . Bull. Sc. Math. , 107 : 345 – 370 .
  • Gray , A. and Vanhecke , L. 1979 . Riemannian geometry as determined by the volumes of small geodesic balls . Acta. Math. , 142 : 157 – 198 .
  • Kim , Y.T. and Park , H.S. 2002 . Mean distance of Brownian motion on a Riemannian manifold . Stoch. Proc. and their Appl. , 102 : 117 – 138 . [CROSSREF]
  • Liao , M. and Zheng , W.A. 1995 . Radial part of Brownian motion on a Riemannian manifold . Ann. of Prob. , 23 ( 1 ) : 173 – 177 .
  • Sakai , T. 1971 . On eigen-values of Laplacian and curvature of Riemannian manifold . Tohoku Math. J. , 23 : 589 – 603 .

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