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Wiener-Hopf factorisation of Brownian motion
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  • Published: September 1989

Wiener-Hopf factorisation of Brownian motion

  • Paul McGill1 

Probability Theory and Related Fields volume 83, pages 355–389 (1989)Cite this article

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Summary

We study how Brownian motion behaves under time change by a fluctuating additive functionalA t , in particular letting τ be the first passage time ofA t to zero we computeP −x[B τ ∈dy] explicitly in certain cases. The calculation is not an easy one, our method uses the Désiré André relation for the overshoot of a Lévy process and depends on some elliptic function identities. This paper only considers the one boundary case whereA t is increasing (resp. decreasing) on the positive (resp. negative) half line.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    Paul McGill

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  1. Paul McGill
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McGill, P. Wiener-Hopf factorisation of Brownian motion. Probab. Th. Rel. Fields 83, 355–389 (1989). https://doi.org/10.1007/BF00964370

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  • Received: 22 December 1986

  • Revised: 19 June 1988

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF00964370

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Mathematical Biology
  • Function Identity
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