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April, 1965 On the Mean Number of Curve Crossings by Non-Stationary Normal Processes
M. R. Leadbetter, J. D. Cryer
Ann. Math. Statist. 36(2): 509-516 (April, 1965). DOI: 10.1214/aoms/1177700160


In this paper we consider the mean number of crossings of an arbitrary curve, in a given time $T$, by a non-stationary normal process. A formula (2) is obtained for this and sufficient conditions for its validity given. These conditions concern the behaviour of the covariance function of the normal process. Incidental results include sufficient conditions for continuity of a normal (non-stationary) process $x(t)$ and also for $x(t)$ to satisfy a Holder condition.


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M. R. Leadbetter. J. D. Cryer. "On the Mean Number of Curve Crossings by Non-Stationary Normal Processes." Ann. Math. Statist. 36 (2) 509 - 516, April, 1965.


Published: April, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0138.11004
MathSciNet: MR174085
Digital Object Identifier: 10.1214/aoms/1177700160

Rights: Copyright © 1965 Institute of Mathematical Statistics


Vol.36 • No. 2 • April, 1965
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