Excursions in Brownian motion
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This article is published in Arkiv för Matematik.The article was published on 1976-12-01 and is currently open access. It has received 222 citations till now. The article focuses on the topics: Brownian motion.read more
Citations
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Journal IssueDOI
Random cutting and records in deterministic and random trees
TL;DR: The number of cuts is equal (in distribution) to the number of records in the tree when edges (or vertices) are assigned random labels when edges are assignedrandom labels.
Journal ArticleDOI
Kac's formula, levy's local time and brownian excursion
J. Appl,Guy Louchard +1 more
TL;DR: In this paper, Kac's formula for Brownian functionals and Levy's local time decomposition are shown to be useful tools in analysing Brownian excursion properties, such as maximum, local time and area distributions.
Posted Content
Scaling limits of random trees and planar maps
TL;DR: In this paper, the scaling limits of random trees and planar maps are discussed in a series of lectures given at the Clay Mathematical Institute Summer School in Buzios, Greece.
Journal ArticleDOI
Infinitely Divisible Laws Associated with Hyperbolic Functions
Jim Pitman,Marc Yor +1 more
TL;DR: The infinitely divisible distributions of random variables with Laplace transforms are characterized for various in a number of different ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their Levy measures, by recursions for their Mellin transforms, and by differential equations satisfied by their Laplace transform.
Journal ArticleDOI
Excursions of Brownian motion and bessel processes
Ronald K. Getoor,M. J. Sharpe +1 more
References
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Book
Diffusion Processes and their Sample Paths
Kiyosi Itô,Henry P. McKean +1 more
TL;DR: In this article, the authors consider the problem of approximating the Brownian motion by a random walk with respect to the de Moivre-laplace limit theorem and show that it is NP-hard.
Journal Article
Sur certains processus stochastiques homogènes
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.compositio.org/legal.php).
BookDOI
Aufgaben und Lehrsätze aus der Analysis: Erster Band: Reihen · Integralrechnung Funktionentheorie
Book
Brownian motion and diffusion
TL;DR: The book as discussed by the authors is part of a trilogy covering the field of Markov processes and provides a readable and constructive treatment of Brownian motion and diffusion, which dispenses with most of the customary transform apparatus.
Journal ArticleDOI
Functional Central Limit Theorems for Random Walks Conditioned to Stay Positive
TL;DR: In this article, it was shown that the conditional and unconditional weak limit for a sequence of independent, identically distributed random variables is the same as that of the standard Brownian motion.