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Regularity of Gaussian Processes on Dirichlet spaces

Author

Listed:
  • 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)

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

Suggested Citation

  • Gérard Kerkyacharian, & Shigeyoshi Ogawa & Pencho Petrushev & Dominique Picard, 2017. "Regularity of Gaussian Processes on Dirichlet spaces," Working Papers 2017-90, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-90
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