Mean-Square Continuity on Homogeneous Spaces of Compact Groups

Domenico Marinucci (1) , Giovanni Peccati (2)

1 DIPMAT - Dipartimento di Matematica [Roma II]
2 FSTC - Faculté des Sciences, de la Technologie et de la Communication

We show that any finite-variance, isotropic random field on a compact group is necessarily mean-square continuous, under standard measurability assumptions. The result extends to isotropic random fields defined on homogeneous spaces where the group acts continuously.

Mots clés: Mean-Square Continuity; Random Processes; Isotropy; Mean-Square Continuity.

Domaines: Probabilités [math.PR]

Domenico Marinucci, Giovanni Peccati. Mean-Square Continuity on Homogeneous Spaces of Compact Groups. 2013. ⟨hal-00746637v2⟩