Accession Number : AD0695688

Title :   ABSTRACT WIENER PROCESSES AND THEIR REPRODUCING KERNEL HILBERT SPACES.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Kallianpur,G.

Report Date : 08 AUG 1969

Pagination or Media Count : 37

Abstract : The paper explores the relationship between Gaussian processes and their associated RKH Spaces. A simple proof of Gross's theorem on abstract Wiener spaces is given. For a Gaussian measure mu with continuous covariance R defined on the Banach space C(T) of real continuous functions on T (T being a separable complete metric space) it is shown that the closure of H(R) in C(T) is the support of mu. This result is extended to Gaussian measures on arbitrary separable Banach spaces. A necessary and sufficient criterion for a separable Gaussian process x(t) (0 = or < t = or < 1) with continuous covariance R to have continuous sample paths is furnished by the following result to the effect that the canonical normal distribution on H(R) extends to a Gaussian measure on C(0,1) if and only if the sup-norm on H(R) is measurable in the sense of Gross. (Author)

Descriptors :   (*STOCHASTIC PROCESSES, *MEASURE THEORY), STATISTICAL PROCESSES, HILBERT SPACE, TOPOLOGY, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE