The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 37, Number 1 (1966), 260-267.
On Crossings of Levels and Curves by a Wide Class of Stochastic Processes
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  and Ylvisaker  for stationary normal processes, to nonstationary and non normal cases. In particular the corresponding result given by Leadbetter and Cryer  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.
Ann. Math. Statist., Volume 37, Number 1 (1966), 260-267.
First available in Project Euclid: 27 April 2007
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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