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Multifractal products of stochastic processes: construction and some basic properties

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Petteri Mannersalo ,
Ilkka Norros  and
Rudolf H. Riedi
Petteri Mannersalo*
Affiliation:
VTT Technical Research Centre of Finland
Ilkka Norros*
Affiliation:
VTT Technical Research Centre of Finland
Rudolf H. Riedi*
Affiliation:
Rice University
*
∗ Postal address: VTT Information Technology, PO Box 1202, FIN-02044 VTT, Finland.
∗ Postal address: VTT Information Technology, PO Box 1202, FIN-02044 VTT, Finland.
∗∗∗ Postal address: Department of Electrical and Computer Engineering, Digital Signal Processing Group, Rice University, MS 380, Houston, TX 77251-1892, USA.
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Abstract

In various fields, such as teletraffic and economics, measured time series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a nonstationary process. To overcome this problem, we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a special form of T-martingales. We study the ℒ2-convergence, nondegeneracy, and continuity of the limit process. Establishing a power law for its moments, we obtain a formula for the multifractal spectrum and hint at how to prove the full formalism.

Keywords

Stochastic processesrandom measuresmultifractalsteletraffic modeling

MSC classification

Primary: 60G57: Random measures
Secondary: 60G30: Continuity and singularity of induced measures

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 4 , December 2002 , pp. 888 - 903
Copyright
Copyright © Applied Probability Trust 2002 

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