Multifractional, multistable, and other processes with prescribed local form

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