Accession Number:

AD0734650

Title:

Gaussian Measures on L sup P Spaces, 1 Less than or Equal to p Less than Infinity,

Descriptive Note:

Corporate Author:

NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1971-11-01

Pagination or Media Count:

59.0

Abstract:

One of the main ideas in the paper is to establish a one to one correspondence between Gaussian measures on L sub p, 1 or p infinity, and Gaussian stochastic processes with sample paths in L sub p. This idea is used to prove a number of interesting results about Gaussian measures on L sub p. Using a recent result of Jain and Kallianpur, a zero-one law for Gaussian measures on Frechet spaces is proved, which is subsequently applied to obtain two other zero-one laws. In the first, it is shown that the smaple paths of a zero-mean measurable Gaussian stochastic process belong to L sub p with probability zero or one and in the second, it is shown that a certain random series converges uniformly, on any Borel subset of the real line, with probability zero or one. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE