id: 06126571
dt: j
an: 
au: Le Guével, R.; Véhel, J.Lévy
ti: A Ferguson-Klass-LePage series representation of multistable
    multifractional motions and related processes.
so: Bernoulli 18, No. 4, 1099-1127 (2012).
py: 2012
pu: International Statistical Institute (ISI), Voorburg; Bernoulli Society for
    Mathematical Statistics and Probability, Voorburg
la: EN
cc: 60
ut: Ferguson-Klass-LePage series representation; localisable processes;
    multifractional processes; stable processes
ci: 
li: euclid:bj/1352727803 doi:10.3150/11-BEJ372
ab: Summary: 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. In (J. Theoret. Probab. 22 (2009)
    375-401), a particular way of constructing such processes was
    investigated, leading in particular to multifractional multistable
    processes, which were built using sums over Poisson processes. We
    present here a different construction of these processes, based on the
    Ferguson-Klass-LePage series representation of stable processes. We
    consider various particular cases of interest, including multistable
    Lévy motion, multistable reverse Ornstein-Uhlenbeck process,
    log-fractional multistable motion and linear multistable
    multifractional motion. We also show that the processes defined here
    have the same finite dimensional distributions as the corresponding
    processes built in (J. Theoret. Probab. 22 (2009) 375-401). Finally, we
    display numerical experiments showing graphs of synthesized paths of
    such processes.
rv: