Multifractional Brownian motions indexed by a metric space with distances of negative type

Jacques Istas (1)

1 IPS - Inférence Processus Stochastiques

We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.

Mots clés: Fractional Brownian motion; self-similarity; complex variations; H-sssi processes

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

Jacques Istas. Multifractional Brownian motions indexed by a metric space with distances of negative type. ESAIM: Probability and Statistics, 2013, 17, pp.219-223. ⟨10.1051/ps/2011157⟩. ⟨hal-00851601⟩