Journal of Probability and Statistics
Volume 2010 (2010), Article ID 807491, 26 pages
doi:10.1155/2010/807491
Research Article

Multifractal Analysis of Infinite Products of Stationary Jump Processes

Petteri Mannersalo,1 Ilkka Norros,2 and Rudolf H. Riedi3,4

1VTT Technical Research Centre of Finland, P.O. Box 1100, 90571 Oulu, Finland
2VTT Technical Research Centre of Finland, P.O. Box 1000, 02044 VTT, Finland
3Department of Statistics, Rice University, MS 138, 6100 Main Street Houston, TX 77251-1892, USA
4Ecole d'ingénieurs et d'architectes de Fribourg, Bd de Pérolles 80 - CP 32, CH-1705 Fribourg, Switzerland

Received 21 August 2009; Revised 28 February 2010; Accepted 31 March 2010

Academic Editor: Tomasz J. Kozubowski

Copyright © 2010 Petteri Mannersalo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

There has been a growing interest in constructing stationary measures with known multifractal properties. In an earlier paper, the authors introduced the multifractal products of stochastic processes (MPSP) and provided basic properties concerning convergence, nondegeneracy, and scaling of moments. This paper considers a subclass of MPSP which is determined by jump processes with i.i.d. exponentially distributed interjump times. Particularly, the information dimension and a multifractal spectrum of the MPSP are computed. As a side result it is shown that the random partitions imprinted naturally by a family of Poisson point processes are sufficient to determine the spectrum in this case.