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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Some results on the Brownian meander with drift
Francesco Iafrate,Enzo Orsingher +1 more
Abstract: In this paper we study the drifted Brownian meander, that is a Brownian motion starting from $ u $ and subject to the condition that $ \min_{ 0\leq z \leq t} B(z)> v $ with $ u > v $. The limiting process for $ u \downarrow v $ is analyzed and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.
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The Value of the High, Low and Close in the Estimation of Brownian Motion: Extended Version
TL;DR: In this paper, the conditional expectation and conditional variance of Brownian motion are evaluated subject to one or more of the the close (final value), the high (maximum), the low (minimum), and the intermediate values.
ON TWE RENlARRABLE DISTRIBUTIONS OF MAXIPMA OF SOWIE mAGMENTS OF THE STANI)ARD REFLECTING OM WALK AND BROWNIAN MOTION
TL;DR: In this paper, some distributions of maxi- ma of excursions and related variables for standard random walk and Brownian motion were considered and the infinite divisibility properties of these distributions were discussed.
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Height and diameter of brownian tree
TL;DR: In this paper, the authors provided an explicit formula for the joint law of the height and diameter of the Brownian tree, which is a new result, based on the normalized Brownian excursion.
Special Topic: Bienaymé–Galton–Watson Simple Branching Process and Excursions
TL;DR: In this article, the tree contours and heights are identified as two natural discrete parameter stochastic processes associated with the branching process introduced in Chapter 14 as a probability distribution on a metric space of family 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.
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.