Multifractal analysis of infinite products of stationary jump processes

Petteri Mannersalo, Ilkka Norros, Rudolf H Riedi

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Article number807491
Number of pages26
JournalJournal of Probability and Statistics
Volume2010
DOIs
Publication statusPublished - 2010
MoE publication typeA1 Journal article-refereed

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Multifractal Analysis
Jump Process
Infinite product
Stationary Process
Stochastic Processes
Random Partitions
Stationary Measure
Multifractal Spectrum
Poisson Point Process
Nondegeneracy
Convergence Properties
Scaling
Sufficient
Moment

Cite this

Mannersalo, Petteri ; Norros, Ilkka ; Riedi, Rudolf H. / Multifractal analysis of infinite products of stationary jump processes. In: Journal of Probability and Statistics. 2010 ; Vol. 2010.
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Multifractal analysis of infinite products of stationary jump processes. / Mannersalo, Petteri; Norros, Ilkka; Riedi, Rudolf H.

In: Journal of Probability and Statistics, Vol. 2010, 807491, 2010.

Research output: Contribution to journalArticleScientificpeer-review

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