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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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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