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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