J. Levy Vehel

Multifractional, multistable, and other processes with prescribed local form

We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional $α$-stable processes, and 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.