Brownian Manifolds, Negative Type and Geo-temporal Covariances

• DOI: 10.31390/cosa.10.4.03
• Publication Date: 2018-06-06T16:05:02Z
• 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/>