Multifractal scaling of products of birth--death processes
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 R\'{e}nyi functions and dependence properties.
Keywords
Cite
@article{arxiv.0906.2277,
title = {Multifractal scaling of products of birth--death processes},
author = {Vo V. Anh and Nikolai N. Leonenko and Narn-Rueih Shieh},
journal= {arXiv preprint arXiv:0906.2277},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.3150/08-BEJ156 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)