Multifractal products of stochastic processes: Construction and some basic properties

Petteri Mannersalo, Ilkka Norros, Rudolf H. Riedi

Research output: Contribution to journalArticleScientificpeer-review

24 Citations (Scopus)

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 non-stationary 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 L2-convergence, non-degeneracy 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.
Original languageEnglish
Pages (from-to)888-903
JournalAdvances in Applied Probability
Volume34
Issue number4
DOIs
Publication statusPublished - 2002
MoE publication typeA1 Journal article-refereed

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