
Accession Number : AD0722079
Title : Representation of Stochastic Processes of Second Order and Linear Operations,
Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS
Personal Author(s) : Cambanis,Stamatis
Report Date : FEB 1971
Pagination or Media Count : 26
Abstract : Series representations are obtained for the entire class of measurable, second order stochastic processes defined on any interval of the real line. They include as particular cases all earlier representations; they suggest a notion of 'smoothness' that generalizes well known continuity notions; and they decompose the stochastic process into two orthogonal parts, the smooth part and a strongly discontinuous part. Also linear operations on measurable, second order processes are studied; it is shown that all 'smooth' linear operations on a process, and in particular all linear operations on a 'smooth' process, can be approximated arbitrarily closely by linear operations on the sample paths of the process. (Author)
Descriptors : (*STOCHASTIC PROCESSES, THEOREMS), INFORMATION THEORY, TRANSFORMATIONS(MATHEMATICS), APPROXIMATION(MATHEMATICS), MEASURE THEORY, SERIES(MATHEMATICS), SET THEORY
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE