Open AccessA Ferguson–Klass–LePage series representation of multistable multifractional motions and related processes
Author(s) -
Ronan Le Guével,
Jacques Lévy Vehel
Publication year - 2012
Publication title -
bernoulli
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.814
H-Index - 72
eISSN - 1573-9759
pISSN - 1350-7265
DOI - 10.3150/11-bej372
Subject(s) - series (stratigraphy) , representation (politics) , mathematics , motion (physics) , process (computing) , statistical physics , classical mechanics , computer science , physics , paleontology , politics , political science , law , biology , operating system
International audienceThe 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 Lévy 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