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
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Pattern-avoiding permutations and Brownian excursion Part I: Shapes and fluctuations
TL;DR: In this article, the scaling limits of a random permutation avoiding a pattern of length 3 and their relation to Brownian excursion are investigated, and the connection between permutations that avoid given patterns and their relations to Brownians is explored.
Book ChapterDOI
Diffusions, Markov Processes, and Martingales: Preface to the Second Edition
L. C. G. Rogers,David Williams +1 more
Book ChapterDOI
The height and width of simple trees
TL;DR: The limit law of the couple height-width for simple trees can be seen as a consequence of deep results of Aldous, Drmota and Gittenberger, and Jeulin this article.
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The effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian
TL;DR: In this paper, the average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0, L] is derived, relying on the eigenvalue distributions (extreme value statistics problem) which are obtained explicitly.
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Excursion and meander in random walk
Endre Csáki,Sri Gopal Mohanty +1 more
TL;DR: In this paper, Bernoulli bridge, excursion and meander are defined on the symmetric random walk similarly to Brownian bridge and excursion, and their limits are obtained using weak convergence.
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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.