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Multifractional, multistable, and other processes with prescribed local form

Research output: Contribution to journalArticle

Author(s)

Kenneth John Falconer, J Lévy Véhel

School/Research organisations

Abstract

We present a general method for constructing stochastic processes with prescribed local form, encompassing examples such as variable amplitude multifractional Brownian and multifractional alpha-stable processes. We apply the method to Poisson sums to construct multistable processes, that is, processes that are locally alpha(t)-stable but where the stability index alpha(t) varies with t. In particular we construct multifractional multistable processes, where both the local self-similarity and stability indices vary.

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Details

Original languageEnglish
Pages (from-to)375-401
Number of pages27
JournalJournal of Theoretical Probability
Volume22
Issue number2
DOIs
Publication statusPublished - Jun 2009

    Research areas

  • Stochastic process, Localisable, Multifractional, Multistable, Stable process, FRACTIONAL BROWNIAN MOTIONS, STABLE MOTION

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