An estimation of the stability and the localisability functions of multistable processes

Ronan Le Guével (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Multistable processes are tangent at each point to a stable process, but where the index of stability and the index of localisability varies along the path. In this work, we give two estimators of the stability and the localisability functions, and we prove the consistency of those two estimators. We illustrate these convergences with two classical examples, the Levy multistable process and the Linear Multifractional Multistable Motion.

Mots clés: Multistable Levy motion; multistable multifractional processes; L-p consistency; Ferguson-Klass-LePage representation

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Ronan Le Guével. An estimation of the stability and the localisability functions of multistable processes. Electronic Journal of Statistics , 2013, 7, pp.1129-1166. ⟨10.1214/13-EJS797⟩. ⟨hal-00480881v3⟩