• Bernoulli
  • Volume 15, Number 2 (2009), 508-531.

Multifractal scaling of products of birth–death processes

Vo V. Anh, Nikolai N. Leonenko, and Narn-Rueih Shieh

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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.

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Bernoulli, Volume 15, Number 2 (2009), 508-531.

First available in Project Euclid: 4 May 2009

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geometric birth–death processes log-binomial scenario log-Pascal scenario log-Poisson scenario multifractal products


Anh, Vo V.; Leonenko, Nikolai N.; Shieh, Narn-Rueih. Multifractal scaling of products of birth–death processes. Bernoulli 15 (2009), no. 2, 508--531. doi:10.3150/08-BEJ156.

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