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
Limit distributions for the Bernoulli meander
TL;DR: In this paper, the authors studied the limit behavior of the distributions and the moments of the Bernoulli meander in the case where the number of steps in the random walk tends to infinity.
Journal ArticleDOI
Parking Functions, Empirical Processes, and the Width of Rooted Labeled Trees
TL;DR: This paper provides tight bounds for the moments of the width of rooted labeled trees with $n$ nodes, answering an open question of Odlyzko and Wilf (1987).
Journal ArticleDOI
Some asymptotic properties of the local time of the uniform empirical process
Miklos Csorgo,Zhan Shi,Marc Yor +2 more
TL;DR: In this paper, the authors studied the asymptotic properties of the local time of the uniform empirical process and obtained two versions of the law of the iterated logarithm for the integral of the square of local time.
Book ChapterDOI
The distribution of local times of a Brownian bridge
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/conditions) of the agreement with the séminaire de probabilités (Strasbourg) are discussed.
Journal ArticleDOI
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, a class which includes the Rayleigh, half-normal and gamma distributions.
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.