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An extension of a result of Burdzy and Lawler
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  • Published: December 1991

An extension of a result of Burdzy and Lawler

  • M. C. Cranston1 &
  • T. S. Mountford2 

Probability Theory and Related Fields volume 89, pages 487–502 (1991)Cite this article

Summary

It is shown that for all mean zero, finite variance random walks, the critical non-intersection exponents are equal to those for Brownian motion. The method uses the local time of intersection.

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References

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  • Durett, R.: Stochastic processes: theories and examples. Monterey: Wadsworth 1989

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  • Dynkin, E.: Self intersection gauge. Ann. Probab.16, 1–57 (1988)

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  • LeGall, J.F.: Proprietes d'Intersection des Marches alleatoire I, II. Commun. Math. Phys.104, 471–507 (1987)

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  • Port, S., Mountford, T.: Some Brownian path properties. (preprint 1991)

  • Williams, D.: Path decomposition and continuity of local time for one-dimensional diffusions I. Proc. Lond. Math. Soc., III Ser.26, 738–768 (1974)

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rochester, 14627, Rochester, NY, USA

    M. C. Cranston

  2. Department of Mathematics, University of California, 90024, Los Angeles, CA, USA

    T. S. Mountford

Authors
  1. M. C. Cranston
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  2. T. S. Mountford
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Additional information

Research supported by grants from NSA and NSF

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Cite this article

Cranston, M.C., Mountford, T.S. An extension of a result of Burdzy and Lawler. Probab. Th. Rel. Fields 89, 487–502 (1991). https://doi.org/10.1007/BF01199790

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  • Received: 06 December 1989

  • Revised: 10 April 1991

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01199790

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Local Time
  • Mathematical Biology
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