Multifractional, Multistable, and Other Processes with Prescribed Local Form

K. J. Falconer () and J. Lévy Véhel ()
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K. J. Falconer: University of St Andrews
J. Lévy Véhel: INRIA Rocquencourt

Journal of Theoretical Probability, 2009, vol. 22, issue 2, 375-401

Abstract: Abstract 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.

Keywords: Stochastic process; Localisable; Multifractional; Multistable; Stable process (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10959-008-0147-9

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