Gaussian processes on compact symmetric spaces

  • R. Askey
  • N. H. Bingham


Paul Lévy studied Gaussian processes ξ(a) with the parameter a running over Euclidean d-space R d and he also studied the case when a runs over the d-sphere S d . His results were extended by Gangolli in a number of directions, one being the extension to the cases where the parameter a lies in the other two-point homogeneous Riemannian manifolds. In the compact cases Gangolli showed there was a distinction between spheres and projective spaces, in that the process discovered by Lévy which he called Brownian motion parametrized by spheres does not exist for projective spaces. However many interesting Gaussian process exist with parameters running through projective spaces as we show.


Manifold Stochastic Process Brownian Motion Probability Theory Riemannian Manifold 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • R. Askey
    • 1
  • N. H. Bingham
    • 2
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of Mathematics, Westfield CollegeUniversity of LondonLondonEngland

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