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Occupation times of stationary gaussian processes

Published online by Cambridge University Press:  14 July 2016

Simeon M. Berman
Simeon M. Berman*
Affiliation:
New York University
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Abstract

Let X(t), t ≧ 0, be a stationary Gaussian process with zero mean, unit variance and continuous covariance function r(t). Suppose that, for some ε > 0 so that there is a version of the process whose sample functions are continuous [1].

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 721 - 733
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Beljaev, Y. K. (1961) Continuity and Holder's conditions for sample functions of stationary Gaussian processes. Proc. Fourth Berkeley Symp. Math. Statist. and Prob. 2, University of California Press.Google Scholar
[2] Cramèr, H. (1946) Mathematical Methods of Statistics. Princeton University Press, Princeton.Google Scholar
[3] Cramèr, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes: Sample Function Properties and their Applications. John Wiley, New York.Google Scholar
[4] Malevic, T. L. (1969) Asymptotic normality of the number of crossings of the zero level by a Gaussian process. Teor. Veroyat. Primen. 14, 292–301. (In Russian.).Google Scholar
[5] Volkonskii, V. A. and Rozanov, Y. A. (1959), (1961) Some limit theorems for random functions I, II. Theor. Probability Appl. 4, 178–197, 6, 186–198.CrossRefGoogle Scholar