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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Dissertation
Random fractal dendrites
TL;DR: In this paper, the authors investigated the physical characteristics of various random fractal versions of this type of set and showed that the scaling factors of these recursively defined structures form what is known as a multiplicative cascade.
Posted Content
Brownian excursions in a corridor and related Parisian options
Angelos Dassios,Shanle Wu +1 more
TL;DR: In this paper, the authors studied the excursion time of a Brownian motion with drift inside a corridor by using a four states semi-Markov model and obtained an explicit expression for the Laplace transform of its price formula.
Journal Article
Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude
Jim Pitman,Marc Yor +1 more
TL;DR: In this paper, the authors give new proofs of Cs aki's formula for the law of the ratio 1, Q of the maximum relative to the amplitude for a standard Brownian bridge.
Book ChapterDOI
Patterns in Random Walks and Brownian Motion
Jim Pitman,Wenpin Tang +1 more
TL;DR: In this paper, it is shown that it is possible to find continuous paths of unit length in linear Brownian motion, and the asymptotics of the expected waiting time for several interesting patterns are derived.
Journal ArticleDOI
The Laws of Chung and Hirsch for Cauchy's Principal Values Related to Brownian Local Times
TL;DR: Two Chung-type and Hirsch-type laws are established to describe the liminf asymptotic behaviours of the Cauchy's principal values related to Brownian local times 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.