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
On excursions inside an excursion
May-Ru Chen,Ju-Yi Yen +1 more
TL;DR: In this paper, the authors considered excursions of a Brownian excursion above a random level x, where x is the value of the excursion at an independent uniform time on [0, 1].
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Local equilibrium in planar non interacting particle systems
Péter Nándori,Trevor Teolis +1 more
TL;DR: In this paper, the authors identify a set of abstract conditions which imply the local equilibrium of the particle density in diffusive scaling limit and verify that their abstract conditions hold in two examples: i.e., random walks and the periodic Lorentz process.
Book ChapterDOI
Paul Lévy’s Way to His Local Time
A. A. Balkema,Kai Lai Chung +1 more
TL;DR: In this article, the notion of local time for Brownian motion was introduced, and Levy gave several equivalent definitions, and towards the end of that long paper he proved the following result.
Book ChapterDOI
From the Original (1979) Preface
TL;DR: In this paper, the authors used the preface to their definitive account of stochastic integral theory, which is called First Intuitive Markov Process Theory (FIMT).
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.