Mean-square continuity on homogeneous spaces of compact groups. (English) Zbl 1329.60139

Marinucci, Domenico; Peccati, Giovanni

Electron. Commun. Probab. 18, Paper No. 37, 10 p. (2013).

Summary: 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.

MSC:

60G60

Random fields

Keywords:

isotropic random fields; compact groups; mean-square continuity; homogeneous spaces