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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Excursions Above the Minimum for Diffusions
TL;DR: In this article, the existence of a Lévy system for the excursions of a one-dimensional diffusion process above its past-minimum process was shown in both a global and a local form.
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Random real trees
TL;DR: A survey of recent developments about real trees can be found in this paper, where the authors briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees.
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Generalized gamma approximation with rates for urns, walks and trees
TL;DR: In this article, a new class of time inhomogeneous Polya-type urn schemes and optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters were studied.
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Precise logarithmic asymptotics for the right tails of some limit random variables for random trees
James Allen Fill,Svante Janson +1 more
TL;DR: In this paper, the authors obtained precise asymptotics for the logarithm of the right-hand tail of a random finite tree for certain random variables that arise as limits of functionals of random finite trees.
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.
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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.