Multifractional, multistable, and other processes with prescribed local form

Kenneth John Falconer, J Lévy Véhel

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

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.

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

Keywords

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

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