A Ferguson-Klass-LePage series representation of multistable multifractional processes and related processes

Abstract

The study of non-stationary processes whose local form has controlled properties is a fruitful and important area of research, both in theory and applications. We present here a construction of multifractional multistable processes, based on the Ferguson-Klass-LePage series representation of stable processes. We consider various particular cases of interest, including multistable L\'evy motion, multistable reverse Ornstein-Uhlenbeck process, log-fractional multistable motion and linear multistable multifractional motion. We also compute the finite dimensional distributions of those processes. Finally, we display numerical experiments showing graphs of synthesized paths of such processes.