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Another Look at Williams’ Decompostion Theorem

  • P. J. Fitzsimmons
Part of the Progress in Probability and Statistics book series (PRPR, volume 12)

Abstract

In studying the excursions of a diffusion process above its past minimum level, we have discovered a conceptually simple proof of Williams’ decomposition [5] of a transient diffusion at its global minimum. We use an approximation argument based on the trivial observation that the minimum level of the diffusion is the smallest y such that Ty < +∞, TY- = +∞, where TY is the hitting time of y.

Keywords

Compact Subset Global Minimum Simple Proof Exit Time Brownian Bridge 
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References

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    P. A. Meyer, R. T. Smythe and J. B. Walsh. Birth and death of Markov processes. Proc. 6th Berk. Symp. Stat. Prob., Vol. III, 295–305. Univ. of Cal. Press, 1972.Google Scholar
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    D. Williams. Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc. (3) 28 (1974), 738–768.MathSciNetMATHCrossRefGoogle Scholar
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    W. Vervaat. A relation between Brownian bridge and Brownian excursion. Ann. Prob., 7 (1979), 143–149.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • P. J. Fitzsimmons
    • 1
  1. 1.Department of Mathematical SciencesThe University of AkronAkronUSA

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