Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T22:54:56.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple trigonometric models for narrow-band stationary processes

Published online by Cambridge University Press:  14 July 2016

A. M. Hasofer
Get access Rights & Permissions [Opens in a new window]

Abstract

Over a finite interval, a Gaussian stationary process can be approximated by a finite trigonometric sum, and the error introduced by the approximation can be exactly bounded, as far as the distribution of the upper tail of the maximum is concerned. A simple case is exhibited, where a narrow band process is well approximated by means of a two-term trigonometric representation.

Keywords

GAUSSIAN PROCESSDISTRIBUTION OF MAXIMUMNARROW-BAND PROCESSESFOURIER SERIES
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 333 - 343
Copyright
Copyright © 1982 Applied Probability Trust 

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.)

References

Berman, S. M. (1971) Excursions above high levels for stationary Gaussian processes. Pacific J. Math. 36, 63–79.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Blake, I. F. and Lindsay, W. C. (1973) Level-crossing problems for random processes. IEEE Trans. Information Theory IT–19, 295–315.CrossRefGoogle Scholar
Chung, K. L. (1968) A Course in Probability Theory. Harcourt, Brace and World, New York.Google Scholar
Churchill, R. V. (1969) Fourier Series and Boundary Value Problems. McGraw-Hill, New York.Google Scholar
Cramer, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
Gnedenko, B. V. (1962) Theory of Probability. Chelsea, New York.Google Scholar
Pakula, L. (1976) Representation of stationary Gaussian processes on a finite interval. IEEE Trans. Information Theory IT-22, 231–232.CrossRefGoogle Scholar
Shepp, A. and Slepian, D. (1976) First passage time for a particular stationary periodic Gaussian process. J. Appl. Prob. 13, 27–38.CrossRefGoogle Scholar
Vanmarke, H. E. (1975) On the distribution of the first passage time for normal stationary random processes. J. Appl. Mech., Trans. Amer. Soc. Mech. Eng. 42, 215–220.CrossRefGoogle Scholar
Wong, E. (1971) Stochastic Processes in Information and Dynamical Systems. McGraw-Hill, New York.Google Scholar