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February, 1966 On Crossings of Levels and Curves by a Wide Class of Stochastic Processes
M. R. Leadbetter
Ann. Math. Statist. 37(1): 260-267 (February, 1966). DOI: 10.1214/aoms/1177699615


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.


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M. R. Leadbetter. "On Crossings of Levels and Curves by a Wide Class of Stochastic Processes." Ann. Math. Statist. 37 (1) 260 - 267, February, 1966.


Published: February, 1966
First available in Project Euclid: 27 April 2007

zbMATH: 0141.14906
MathSciNet: MR208667
Digital Object Identifier: 10.1214/aoms/1177699615

Rights: Copyright © 1966 Institute of Mathematical Statistics

Vol.37 • No. 1 • February, 1966
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