Another Look at Williams’ Decompostion Theorem

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


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.


Compact Subset Global Minimum Simple Proof Exit Time Brownian Bridge 
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  1. 1.
    K. Ito and H. P. McKean. Diffusion Processes and their Sample Paths. Springer-Verlag, Berlin, 1965.MATHGoogle Scholar
  2. 2.
    B. Maisonneuve. Exit Systems. Ann. Prob., 3(1975), 399–411.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    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
  4. 4.
    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
  5. 5.
    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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