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

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)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0616762

Entities

People

  • M. R. Leadbetter

Organizations

  • RTI International

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Crossings
  • Probability
  • Stationary
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.