On Crossings of Levels and Curves by a Wide Class of Stochastic Processes
Leadbetter, M. R.
Ann. Math. Statist., Tome 37 (1966) no. 6, p. 260-267 / Harvested from Project Euclid
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.
Publié le : 1966-02-14
Classification: 
@article{1177699615,
     author = {Leadbetter, M. R.},
     title = {On Crossings of Levels and Curves by a Wide Class of Stochastic Processes},
     journal = {Ann. Math. Statist.},
     volume = {37},
     number = {6},
     year = {1966},
     pages = { 260-267},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177699615}
}
Leadbetter, M. R. On Crossings of Levels and Curves by a Wide Class of Stochastic Processes. Ann. Math. Statist., Tome 37 (1966) no. 6, pp.  260-267. http://gdmltest.u-ga.fr/item/1177699615/