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Type: Article
The randomly stopped geometric Brownian motion
Abstract:
In this short note we compute the probability density function of the random variable X-T, where X-t is a geometric Brownian motion, and where T is a random variable independent of X-t and has either a Gamma distribution or it is uniformly distributed. In the last section of the note, the distribution obtained for X-T is fitted to the data consisting in the academic production of a set of mathematicians. (C) 2014 Elsevier B.V. All rights reserved.
In this short note we compute the probability density function of the random variable X-T, where X-t is a geometric Brownian motion, and where T is a random variable independent of X-t and has either a Gamma distribution or it is uniformly distributed. In the last section of the note, the distribution obtained for X-T is fitted to the data consisting in the academic production of a set of mathematicians. (C) 2014 Elsevier B.V. All rights reserved.
Keywords: Power Laws; Heavy Tails; Zipf Law
MSC: 60J65
Journal: Statistics and Probability Letters
ISSN: 1879-2103
Year: 2014
Volume: 90
Pages: 85-92
Created: 2014-05-16 17:36:38
Modified: 2015-03-17 17:05:42
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