Linear Fractional Stable Sheets: wavelet expansion and sample path properties

Antoine Ayache (1) , François Roueff (2) , Yimin Xiao (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 Department of Statistics and Probability (Michigan State University)

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in Ayache, Roueff and Xiao (2007). By using this representation, in the case where the sample paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these paths is obtained as well as an upper bound for their behavior at infinity and around the coordinate axes. The Hausdorff dimensions of the range and graph of these stable random fields are then derived.

Mots clés: Wavelet analysis; stable processes; linear fractional stable sheet; modulus of continuity; Hausdorff dimension

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

Antoine Ayache, François Roueff, Yimin Xiao. Linear Fractional Stable Sheets: wavelet expansion and sample path properties. Stochastic Processes and their Applications, 2009, 119 (4), pp.1168-1197. ⟨10.1016/j.spa.2008.06.004⟩. ⟨hal-00287097⟩