Singularity of Gaussian measures in function spaces with factorable covariance functions

James Juei-Chin Yeh

Vol. 31 (1969), No. 2, 547–554

DOI: 10.2140/pjm.1969.31.547

Abstract

Singularity of Gaussian measures μ₁ and μ₂ on the function space R^IJ of real valued functions x(t) on an arbitrary interval D with factorable covariance functions r_i(s,t), i.e., r_i(s,t) = u_i(s)v_i(t) for s ≤ t and r_i(s,t) = v_i(s)u_i(t) for s ≥ t,i = 1,2, is treated. Local conditions on the factor functions u_i(t) and v_x(t) which insure the singularity of μ₁ and μ₂ are given.

Mathematical Subject Classification

Primary: 60.40

Milestones

Received: 3 April 1969

Published: 1 November 1969