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 ArticleDOI
Brownian bridge asymptotics for random mappings
David Aldous,Jim Pitman +1 more
TL;DR: A new technique is introduced, which starts by specifying a coding of mappings as walks with ± 1 steps as a nonuniform random walk, and the main result is that as n→∞ the random walk rescales to reflecting Brownian bridge.
Journal ArticleDOI
Excursions of a Markov Process
TL;DR: In this paper, the authors compared the excursion straddling $t$ and the first excursion exceeding $u$ in length of a Markov process in a general setting.
Journal Article
Path transformations connecting Brownian bridge, excursion and meander
Jean Bertoin,Jim Pitman +1 more
Abstract: We present a unified approach to numerous path transformations connecting the Brownian bridge, excursion and meander. Simple proofs of known results are given and new results in the same vein are proposed.
Book ChapterDOI
Decomposition at the maximum for excursions and bridges of one-dimensional diffusions
Jim Pitman,Marc Yor +1 more
TL;DR: Ito's theory of excursions has been generalized to excursions of Markov processes away from a set of states [34, 19, 10] and to excursion of stationary, not necessarily Markovian processes as mentioned in this paper.
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.