FIRST PASSAGE TIMES AND THEIR APPLICATIONS TO THE ENGINEERING AND MANAGEMENT SCIENCES.
Abstract
Let X(t) where t is an element of T be a random process defined upon a set S'. A first passage time between two events E and F in S' is the random length T sub EF of the time interval separating the instant at which X(t) first enters F beginning with the instant at which X(t) most recently left E. The process (X(t)) need not be defined in continuous time but possibly only at discrete instants or steps t1, t2, ... , tN arranged in chronological sequence whether equidistant or not. In this case the first passage time T sub EF is defined to be the random number N sub EF (N = 1, 2, ...) of steps or trials, required for the first occurrence of F beginning with the step at which E last occurred. If E = F then T sub EE is called the recurrence time of the event E. In the paper a number of models of random processes are given along with their associated first passage time distributions or the lower order moments thereof. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1969
- Accession Number
- AD0700118
Entities
People
- Richard L. Patterson
Organizations
- University of Florida