On locally self-similar fractional random fields indexed by a manifold

Jacques Istas (1) , Céline Lacaux (2, 3)

1 IPS - Inférence Processus Stochastiques
2 IECL - Institut Élie Cartan de Lorraine
3 BIGS - Biology, genetics and statistics

Local self-similarity for Euclidean random fields has been introduced since a while. In this paper, we define local self-similarity for manifold indexed random fields. We study the properties of the tangent field. In the Gaussian and stable cases, we obtain the expected relations between the fractional index and the stability index. We then give examples.

Mots clés: Local self-similarity; random field; manifold

Domaines: Probabilités [math.PR]

Jacques Istas, Céline Lacaux. On locally self-similar fractional random fields indexed by a manifold. Stochastics: An International Journal of Probability and Stochastic Processes, 2013, 85 (3), pp.489-499. ⟨10.1080/17442508.2012.654609⟩. ⟨hal-00193203v2⟩