  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.
