Weakly orthogonally additive functionals, white noise integrals and linear Gaussian stochastic processes

Jan Rosiński and Wojbor Woyczynski

Vol. 71 (1977), No. 1, 159–172

DOI: 10.2140/pjm.1977.71.159

Abstract

Let E be a Banach space. We prove a representation theorem for functionals on L²(E) that are additive on weakly orthogonal elements (as defind by Beck and Warren in Pacific J. Math. in 1972) and utilize the theorem to obtain a characterization theorem for linear Gaussian stochastic processes on L²(E) that take independent values on weakly orthogonal functions. This enables us give a new and very natural interpretation of the notion of weak orthogonality.

Mathematical Subject Classification 2000

Primary: 60B05

Secondary: 46E99, 60G15

Milestones

Received: 12 May 1976

Revised: 26 October 1976

Published: 1 July 1977