Ball throwing on spheres

Anne Estrade (1) , Jacques Istas (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 SMS - Statistique et Modélisation Stochatisque

Ball throwing on Euclidean spaces has been considered for some time. A suitable renormalization leads to a fractional Brownian motion as limit object. In this paper, we investigate ball throwing on spheres. A different behavior is exhibited: we still get a Gaussian limit, but it is no longer a fractional Brownian motion. However, the limit is locally self-similar when the self-similarity index H is less than 1 / 2.

Keywords: fractional Brownian motion; overlapping balls; scaling; self-similarity; spheres

Domains: Probability [math.PR]

Anne Estrade, Jacques Istas. Ball throwing on spheres. Bernoulli, 2010, 16 (4), pp.953-970. ⟨10.3150/09-BEJ241⟩. ⟨hal-00332812v2⟩