Representation of Stochastic Processes of Second Order and Linear Operations,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1971
- Accession Number
- AD0722079
Entities
People
- Stamatis Cambanis
Organizations
- University of North Carolina at Chapel Hill