Decomposition at the maximum for excursions and bridges of one-dimensional diffusions

Jim Pitman and Marc Yor
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Jim Pitman: University of California, Department of Statistics
Marc Yor: Université Pierre et Marie Curie, Laboratoire de Probabilités

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 293-310 from Springer

Abstract: Abstract In his fundamental paper [25], Itô showed how to construct a Poisson point process of excursions of a strong Markov process X over time intervals when X is away from a recurrent point a of its statespace. The point process is parameterized by the local time process of X at a. Each point of the excursion process is a path in a suitable space of possible excursions of X,starting at a at time 0, and returning to a for the first time at some strictly positive time ζ, called the lifetime of the excursion. The intensity measure of the Poisson process of excursions is a σ-finite measure Λ on the space of excursions, known as Itô’s excursion law. Accounts of Itô’s theory of excursions can now be found in several textbooks [48, 46, 10]. His theory has also been generalized to excursions of Markov processes away from a set of states [34, 19, 10] and to excursions of stationary, not necessarily Markovian processes [38].

Keywords: Brownian Motion; Path Space; Brownian Bridge; Bessel Process; Path Decomposition (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68532-6_19

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DOI: 10.1007/978-4-431-68532-6_19

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