The Annals of Mathematical Statistics

On Crossings of Levels and Curves by a Wide Class of Stochastic Processes

M. R. Leadbetter

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Abstract

In this paper, upcrossings, downcrossings and tangencies to levels and curves are discussed within a general framework. The mean number of crossings of a level (or curve) is calculated for a wide class of processes and it is shown that tangencies have probability zero in these cases. This extends results of Ito [1] and Ylvisaker [7] for stationary normal processes, to nonstationary and non normal cases. In particular the corresponding result given by Leadbetter and Cryer [3] for normal, non stationary processes can be slightly improved to apply under minimal conditions. An application is also given for an important non normal process.

Article information

Source
Ann. Math. Statist., Volume 37, Number 1 (1966), 260-267.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177699615

Digital Object Identifier
doi:10.1214/aoms/1177699615

Mathematical Reviews number (MathSciNet)
MR208667

Zentralblatt MATH identifier
0141.14906

JSTOR
links.jstor.org

Citation

Leadbetter, M. R. On Crossings of Levels and Curves by a Wide Class of Stochastic Processes. Ann. Math. Statist. 37 (1966), no. 1, 260--267. doi:10.1214/aoms/1177699615. https://projecteuclid.org/euclid.aoms/1177699615


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