Counting process

A '''counting process''' is a stochastic process <math>\{N(t), t\geq0\}</math> with values that are non-negative, integer, and non-decreasing:

# <math>N(t)\geq0.</math> # <math>N(t)</math> is an integer. # If <math>s\leq t</math> then <math>N(s)\leq N(t).</math>

If <math>s<t</math>, then <math>N(t)-N(s)</math> is the number of events occurred during the interval <math>(s,t].</math> Examples of counting processes include Poisson processes and Renewal processes.

Counting processes deal with the number of occurrences of something over time. An example of a counting process is the number of job arrivals to a queue over time.

If a process has the Markov property, it is said to be a Markov counting process.

==See also== *Intensity of counting processes *Poisson point process (example for a counting process)

==References==

* Ross, S.M. (1995) ''Stochastic Processes''. Wiley. {{ISBN|978-0-471-12062-9}} * Higgins JJ, Keller-McNulty S (1995) ''Concepts in Probability and Stochastic Modeling''. Wadsworth Publishing Company. {{ISBN|0-534-23136-5}}

Category:Stochastic processes