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Sharp probability estimates for random walks with barriers
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  • Published: 25 July 2008

Sharp probability estimates for random walks with barriers

  • Kevin Ford1 

Probability Theory and Related Fields volume 145, pages 269–283 (2009)Cite this article

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Abstract

We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 273 Altgeld Hall, 1409 West Green St., Urbana, IL, 61801, USA

    Kevin Ford

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  1. Kevin Ford
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Correspondence to Kevin Ford.

Additional information

The author was supported by NSF grants DMS-0301083 and DMS-0555367.

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Cite this article

Ford, K. Sharp probability estimates for random walks with barriers. Probab. Theory Relat. Fields 145, 269–283 (2009). https://doi.org/10.1007/s00440-008-0168-4

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  • Received: 09 December 2007

  • Revised: 02 May 2008

  • Published: 25 July 2008

  • Issue Date: September 2009

  • DOI: https://doi.org/10.1007/s00440-008-0168-4

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Keywords

  • Random walk
  • Barrier
  • Ballot theorems

Mathematics Subject Classification (2000)

  • Primary 60G50
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