Transcription of 1 IEOR 6711: Notes on the Poisson Process
{{id}} {{{paragraph}}}
Example: bachelor of science
1 IEOR 6711: Notes on the Poisson Process
Copyright c 2009 by Karl Sigman 1 IEOR 6711 : Notes on the Poisson Process We present here the essentials of the Poisson point Process with its many interesting properties. As preliminaries, we first define what a point Process is, define the renewal point Process and state and prove the Elementary Renewal Theorem. Point Processes Definition A simple point Process = {tn : n 1} is a sequence of strictly increas- ing points 0 < t1 < t2 < , (1). def with tn as n . With N (0) = 0 we let N (t) denote the number of points that fall in the interval (0, t]; N (t) = max{n : tn t}. {N (t) : t 0} is called the counting Process for.)
1.2 Renewal process A random point process = ft ngfor which the interarrival times fX ngform an i.i.d. sequence is called a renewal process. t n is then called the nth renewal epoch and F(x) = P(X x);x 0;denotes the common interarrival time distribution.
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: