Multiplicity and representation theory of generalized random processes

G. Y. H. Chi

Journal of Multivariate Analysis, 1971, vol. 1, issue 4, 412-432

Abstract: Let (D) be the Schwartz space of infinitely differentiable scalar functions on the line, with compact supports, and ([Omega], [Sigma], P) be a fixed probability space. Let X : (D) --> L2([Omega], [Sigma], P) be a purely nondeterministic generalized random process (g.r.p.) in the sense of Itô with zero mean functional. A multiplicity representation theorem for X is obtained as a result of the Hellinger-Hahn theory. The representation can be assumed to be proper canonical. Thus each g.r.p. determines a unique cardinal number N

Keywords: Deterministic; processes; purely; nondeterministic; processes; multiplicity; harmonizable; tempered; measures; harmonizable; covariance; functional; tempered; covariance; linear; prediction (search for similar items in EconPapers)
Date: 1971
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