Manifold indexed fractional fields

Jacques Istas (1)

1 IPS - Inférence Processus Stochastiques

(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.

Mots clés: Self-similarity; stochastic fields; manifold

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

Jacques Istas. Manifold indexed fractional fields. ESAIM: Probability and Statistics, 2012, 16, pp.222-276. ⟨10.1051/ps/2011106⟩. ⟨hal-00851597⟩