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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Book ChapterDOI
Shifting processes with cyclically exchangeable increments at random
TL;DR: In this paper, a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval is proposed, which is then applied to processes with start and end at zero.
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Some results on the generalized Bronwian meander
Francesco Iafrate,Enzo Orsingher +1 more
TL;DR: In this article, the authors studied the drift Brownian meander with and without drift and provided sufficient conditions for its construction and the distribution of the maximum and first passage times.
Book ChapterDOI
The height and range of watermelons without wall
TL;DR: In this paper, the weak limit of the distribution of the random variables "height" and "range" on the set of p-watermelons without wall restriction was determined.
Journal ArticleDOI
Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
TL;DR: In this paper , the first passage-time properties of diffusion processes with respect to the absorbing boundary condition at position $x = a were formulated as the conditions of the diffusion process's first-passage time properties.
Continuous paths in Brownian motion and related problems
TL;DR: Tang et al. as discussed by the authors studied the problem of finding continuous paths of unit length in linear Brownian motion and derived the asymptotics of the expected waiting time for several interesting patterns.
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.