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.
https://hal.inria.fr/inria-00539033 Contributor : Lisandro FerminConnect in order to contact the contributor Submitted on : Tuesday, November 23, 2010 - 5:16:24 PM Last modification on : Friday, February 4, 2022 - 3:13:12 AM Long-term archiving on: : Thursday, February 24, 2011 - 3:21:36 AM
Kenneth J. Falconer, Jacques Lévy Véhel. Multifractional, multistable, and other processes with prescribed local form. Journal of Theoretical Probability, Springer, 2009, 22 (2), pp.375-401. ⟨10.1007/s10959-008-0147-9⟩. ⟨inria-00539033⟩