Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Continuity Properties of Some Gaussian Processes

Christopher Preston
The Annals of Mathematical Statistics
Vol. 43, No. 1 (Feb., 1972), pp. 285-292
Stable URL: http://www.jstor.org/stable/2239918
Page Count: 8
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Continuity Properties of Some Gaussian Processes
Preview not available

Abstract

Let (S, d) be a compact metric space; let (Ω, F, P) be a probability space, and for each t ∈ S let Xt: Ω → R be a random variable, with E(Xt) = 0 and such that {Xt}t∈ S forms a Gaussian process. In this paper we find sufficient conditions for the Gaussian process {Xt}t∈ S to admit a separable and measurable model whose sample functions are continuous with probability one. The conditions involve the covariance, E(Xs, Xt), of the process and also the ε-entropy of S.

Page Thumbnails

  • Thumbnail: Page 
285
    285
  • Thumbnail: Page 
286
    286
  • Thumbnail: Page 
287
    287
  • Thumbnail: Page 
288
    288
  • Thumbnail: Page 
289
    289
  • Thumbnail: Page 
290
    290
  • Thumbnail: Page 
291
    291
  • Thumbnail: Page 
292
    292