Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields

Hermine Biermé (1) , Céline Lacaux (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 BIGS - Biology, genetics and statistics

In this paper we study modulus of continuity and rate of convergence of series of conditionally sub-Gaussian random fields. This framework includes both classical series representations of Gaussian fields and LePage series representations of stable fields. We enlighten their anisotropic properties by using an adapted quasi-metric instead of the classical Euclidean norm. We specify our assumptions in the case of shot noise series where arrival times of a Poisson process are involved. This allows us to state unified results for harmonizable (multi)operator scaling stable random fields through their LePage series representation, as well as to study sample path properties of their multistable analogous.

Mots clés: Hölder regularity; stable and multistable random fields; sub-Gaussian; operator scaling property

Domaines: Probabilités [math.PR]

Hermine Biermé, Céline Lacaux. Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields. Bernoulli, 2015, 21 (3), pp.1719-1759. ⟨10.3150/14-BEJ619⟩. ⟨hal-00780684v2⟩