Multifractional, Multistable, and Other Processes with Prescribed Local Form

By Kenneth J. Falconer, Jacques Lévy Véhel. 2008

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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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/f7efb033ea56c9d04049348291f1af46bfeaa696