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Exit probability estimates for martingales in geodesic balls, using curvature
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  • Published: June 1992

Exit probability estimates for martingales in geodesic balls, using curvature

  • R. W. R. Darling1 

Probability Theory and Related Fields volume 93, pages 137–152 (1992)Cite this article

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Summary

Kallenberg and Sztencel have recently discovered exponential upper bounds, independent of dimension, on the probability that a vector martingale will exit from a ball in Euclidean space by timet. This article extends their results to martingales on Riemannian manifolds, including Brownian motion, and shows how exit probabilities depend on curvature. Using comparison with rotationally symmetric manifolds, these estimates are easily computable, and are sharp up to a constant factor in certain cases.

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Authors and Affiliations

  1. Mathematics Department, University of South Florida, 33620-5700, Tampa, FL, USA

    R. W. R. Darling

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  1. R. W. R. Darling
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Darling, R.W.R. Exit probability estimates for martingales in geodesic balls, using curvature. Probab. Th. Rel. Fields 93, 137–152 (1992). https://doi.org/10.1007/BF01195225

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  • Received: 07 July 1991

  • Revised: 06 January 1992

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01195225

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Mathematics Subject Classification (1980)

  • 58G32
  • 60G48
  • 60G46
  • 60J65
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