Regularity of Gaussian Processes on Dirichlet spaces

Gérard Kerkyacharian, (), Shigeyoshi Ogawa (), Pencho Petrushev () and Dominique Picard ()
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Gérard Kerkyacharian,: Laboratoire de Probabilités et Modèles aléatoires; Université Paris VII
Shigeyoshi Ogawa: Ritsumeikan University
Pencho Petrushev: University of South Carolina; Interdisciplinary Mathematics Institute
Dominique Picard: Laboratoire de Probabilités et Modèles aléatoires; Université Paris VII

No 2017-90, Working Papers from Center for Research in Economics and Statistics

Abstract: We are interested in the regularity of centered Gaussian processes (Zx(?))x2M indexed by compact metric spaces (M, ?). It is shown that the almost everywhere Besov space regularity of such a process is (almost) equivalent to the Besov regularity of the covarianceK(x, y) = E(ZxZy) under the assumption that (i) there is an underlying Dirichlet structure on M which determines the Besov space regularity, and (ii) the operator K with kernel K(x, y) and the underlying operator A of the Dirichlet structure commute. As an application of this result we establish the Besov regularity of Gaussian processes indexed by compact homogeneous spaces and, in particular, by the sphere. ;Classification-JEL: MSC 58J35 MSC 46E35MSC 42C15MSC 43A85

Keywords: Heat kernel; Gaussian processes; Besov spaces. (search for similar items in EconPapers)
Pages: 38 pages
Date: 2017-08-05
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