Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-04-30T19:34:14.673Z Has data issue: false hasContentIssue false
  • English
  • Français

The envelope of an oscillatory process and its upcrossings

Published online by Cambridge University Press:  01 July 2016

A. M. Hasofer  and
P. Petocz
A. M. Hasofer
Affiliation:
University of New South Wales
P. Petocz
Affiliation:
University of New South Wales
Get access Rights & Permissions [Opens in a new window]

Extract

Let X(t) be a real-valued stochastic process with sample functions which are almost surely continuously differentiable. We say that X(t) has an upcrossing at level u at time t if X(t) = u, X′(t) > 0.

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 711 - 716
Copyright
Copyright © Applied Probability Trust 1978 

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

[1] Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
[2] Leadbetter, M. R. (1966) On crossings of levels and curves by a wide class of stochastic processes. Ann. Math. Statist. 37, 260–267.Google Scholar
[3] Priestley, M. B. (1965) Evolutionary spectra and non-stationary processes. J. R. Statist. Soc. B 27, 204–229.Google Scholar