brownian manifolds negative type and geo temporal covariances

• DOI: 10.48550/arxiv.1612.06431
• Publication Date: 2016-12-01
• Authors: N. H. Bingham; Aleksandar Mijatović; Tasmin L. Symons
• Keywords: Probability (math.PR); FOS: Mathematics; 60D05, 60J65; 0101 mathematics; 01 natural sciences; Mathematics - Probability

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.<br/>12 pages; corrected typos and acknowledgement<br/>