Brownian Manifolds, Negative Type and Geo-temporal Covariances

Abstract

We survey Brownian manifolds -- manifolds that can parametrise Brownian motion -- and those that cannot. We consider covariances of space-time processes, particularly those when space is the sphere -- geo-temporal processes. There are connections with functions of negative type.

arXiv comment12 pages; corrected typos and acknowledgement

References in corpus (3)

• Brownian distance covariance
• Nonstationary covariance models for global data
• The geometry of Brownian surfaces

Cited by in corpus (1)

• Probability, Statistics and Planet Earth, II:The Bochner-Godement theorem for symmetric spaces