Accession Number:

AD0722079

Title:

Representation of Stochastic Processes of Second Order and Linear Operations,

Descriptive Note:

Corporate Author:

NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1971-02-01

Pagination or Media Count:

26.0

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

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE