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Multifractal scaling of products of birth–death processes

Anh, Vo V., Leonenko, Nikolai N. and Shieh, Narn-Rueih 2009. Multifractal scaling of products of birth–death processes. Bernoulli 15 (2) , pp. 508-531. 10.3150/08-BEJ156

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Abstract

We investigate the scaling properties of products of the exponential of birth–death processes with certain given marginal discrete distributions and covariance structures. The conditions on the mean, variance and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We provide four illustrative examples of Poisson, Pascal, binomial and hypergeometric distributions. We establish the corresponding log-Poisson, log-Pascal, log-binomial and log-hypergeometric scenarios for the limiting processes, including their Rényi functions and dependence properties.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: geometric birth–death processes; log-binomial scenario; log-Pascal scenario; log-Poisson scenario; multifractal products
Additional Information: Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/1350-7265/ (accessed 25/02/2014)
Publisher: Bernoulli Society for Mathematical Statistics and Probability
ISSN: 1350-7265
Date of First Compliant Deposit: 30 March 2016
Last Modified: 04 Jun 2017 02:55
URI: http://orca.cf.ac.uk/id/eprint/13906

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