Hostname: page-component-cb9f654ff-9knnw Total loading time: 0 Render date: 2025-08-23T03:30:43.325Z Has data issue: false hasContentIssue false
  • English
  • Français

On random processes that are almost strict sense stationary

Published online by Cambridge University Press:  01 July 2016

Dag Tj⊘stheim
Dag Tj⊘stheim*
Affiliation:
Royal Norwegian Council for Scientific and Industrial Research (NORSAR)
Get access Rights & Permissions [Opens in a new window]

Abstract

An extension of the class of strict sense stationary processes is studied. The extended class represents the strict sense analogy of an extension of wide sense stationary processes considered in an earlier paper [9]. The relations between the various types of processes defined are investigated in the general and in the Gaussian case, and some examples are given. It is shown that associated with a process belonging to the extended class there is a strict sense stationary process. The associated strict sense stationary process is unique iff the original process is ergodic.

Keywords

S.U.B.L.S. PROCESSESU.B.L.S. PROCESSESWIDE SENSE STATIONARYSTRICT SENSE STATIONARYINVARIANT MEASUREGAUSSIAN PROCESSESERGODICITY

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 4 , December 1976 , pp. 820 - 830
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[2] Dowker, Y. N. (1955) On measurable transformations in finite measure spaces. Ann. Math. 62, 504–516.CrossRefGoogle Scholar
[3] Friedman, N. A. (1970) Introduction to Ergodic Theory. Van Nostrand, New York.Google Scholar
[4] Loève, M. (1963) Probability Theory. Van Nostrand, New York.Google Scholar
[5] Priestley, M. B. (1965) Evolutionary spectra and non-stationary processes. J.R. Statist. Soc. B 27, 204–229.Google Scholar
[6] Rozanov, Yu. A. (1967) Stationary Random Processes. Holden Day, San Francisco.Google Scholar
[7] Silverman, R. E. (1957) Locally stationary processes. IRE Trans. Inf. Theory 3, 182–187.Google Scholar
[8] de Sz.-Nagy, B, (1947) On uniformly bounded linear transformations in Hilbert space. Acta Sci. Math. Szeged 11, 152–157.Google Scholar
[9] Tj⊘stheim, D. and Thomas, J. B. (1975) Some properties and examples of random processes that are almost wide sense stationary. IEEE Trans. Inf. Theory 21, 257–262.Google Scholar