Celebratio Mathematica — Yor — Complete Bibliography

Complete Bibliography

Works connected to Nobuyuki Ikeda

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J. Pitman and M. Yor: “Decomposition at the maximum for excursions and bridges of one-dimensional diffusions,” pp. 293–310 in Itô’s stochastic calculus and probability theory. Edited by N. Ikeda. Springer (Tokyo), 1996. Book dedicated to dedicated to Kiyosi Itô on the occasion of his 80th birthday. MR 1439532 Zbl 0877.60053 incollection

In his fundamental paper [1971], 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 \( \zeta \), called the lifetime of the excursion. The intensity measure of the Poisson process of excursions is a \( \sigma \)-finite measure 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 [Rogers and Williams 1987; Revuz and Yor 1994; Blumenthal 1992]. His theory has also been generalized to excursions of Markov processes away from a set of states [Maisonneuve 1975; Getoor and Sharpe 1982; Blumenthal 1992] and to excursions of stationary, not necessarily Markovian processes [Pitman 1986].

James W. Pitman	Related
Nobuyuki Ikeda	Related
Kiyoshi Itō	Related