Incremental moments and Hölder exponents of multifractional multistable processes

Ronan Le Guével (1) , Jacques Lévy Véhel (2, 3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Regularity - Probabilistic modelling of irregularity and application to uncertainties management
3 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

Multistable processes, that is, processes which are, at each ''time'', tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is non constant. In this work, we give further results on (multifractional) multistable processes related to their local structure. We show that, under certain conditions, the incremental moments display a scaling behaviour, and that the pointwise exponent is, as expected, lower than the localisability index.

Mots clés: Pointwise Hölder regularity

Mots clés: Localisable processes; Multistable processes; Multifractional processes; Pointwise Hölder regularity.

Domaines: Probabilités [math.PR]

Ronan Le Guével, Jacques Lévy Véhel. Incremental moments and Hölder exponents of multifractional multistable processes. ESAIM: Probability and Statistics, 2013, 17, pp.135-178. ⟨10.1051/ps/2011151⟩. ⟨inria-00538989⟩