Journal of Theoretical Probability

, Volume 22, Issue 2, pp 375–401 | Cite as

Multifractional, Multistable, and Other Processes with Prescribed Local Form

  • K. J. FalconerEmail author
  • J. Lévy Véhel


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


Stochastic process Localisable Multifractional Multistable Stable process 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of St AndrewsSt Andrews, FifeUK
  2. 2.Projet FractalesINRIA RocquencourtLe Chesnay CedexFrance

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