Another Look at Williams’ Decompostion Theorem
In studying the excursions of a diffusion process above its past minimum level, we have discovered a conceptually simple proof of Williams’ decomposition  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.
KeywordsCompact Subset Global Minimum Simple Proof Exit Time Brownian Bridge
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- 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