The Annals of Mathematical Statistics

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

M. R. Leadbetter

Full-text: Open access


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

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

First available in Project Euclid: 27 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



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.

Export citation