Accession Number : AD0616762

Title :   ON CROSSINGS OF LEVELS AND CURVES BY A WIDE CLASS OF STOCHASTIC PROCESSES.

Descriptive Note : Technical rept.,

Corporate Author : RESEARCH TRIANGLE INST DURHAM N C

Personal Author(s) : Leadbetter,M. R.

Report Date : JUN 1965

Pagination or Media Count : 21

Abstract : In this report definitions are given for crossings, upcrossings and downcrossings of, and tangencies to levels and curves by a process x (t), in a general context. Let C(u) denote the number of crossings of the level u by x (t) in 0 < t < 1. The mean of C(u) is evaluated for a wide class of stochastic processes and it is shown that tangencies to the level u have probability zero under general conditions. Applications are given to non stationary normal processes, and to the (non normal) envelope of a stationary normal process. (Author)

Descriptors :   (*STOCHASTIC PROCESSES, THEORY), DISTRIBUTION THEORY, PROBABILITY, INTEGRAL TRANSFORMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE