Excursions Above the Minimum for Diffusions

P. J. Fitzsimmons

Excursions Above the Minimum for Diffusions

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arxiv 1308.5189 v1 pith:FUSYX2TI submitted 2013-08-23 math.PR

P. J. Fitzsimmons This is my paper · ORCID

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keywords aboveexcursionsprocessapplicationsdecompositiondemonstratediffusiondiffusions

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We demonstrate the existence of a "L\'evy system" for the excursions of a one-dimensional diffusion process above its past-minimum process. As applications we provide a direct proof of D. Williams' decomposition (in both a global and a local form) and of a theorem of W. Vervaat.

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Drawdowns of diffusions
math.PR 2024-11 conditional novelty 6.0 of 10

The authors prove Lehoczky's and Malyutin's drawdown formulas via excursion theory and analyze the Markov process of the maximum at the first drawdown time.

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