Counting process

A counting process is a stochastic process {N(t), t ≥ 0} that possesses the following properties:

1. N(t) ≥ 0.
2. N(t) is an integer.
3. If s ≤ t then N(s) ≤ N(t).

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

Counting processes deal with the number of various outcomes in a system over time. An example of a counting process is the number of occurrences of "heads" over some number of coin tosses.

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

References

• Ross, S.M. (1995) Stochastic Processes. Wiley. ISBN 978-0471120629
• Higgins JJ, Keller-McNulty S (1995) Concepts in Probability and Stochastic Modeling. Wadsworth Publishing Company. ISBN 0-534-23136-5