Multifractal scaling of products of birth--death processes

Details Multifractal scaling of products of birth--death processes Multifractal scaling of products of birth--death processes

2009-06-12

arxiv.org/abs/0906.2277v1

Bernoulli 2009, Vol. 15, No. 2, 508-531

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ156 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ156

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 R\'{e}nyi functions and dependence properties.

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