Counting process
Appearance
A counting process is a stochastic process {N(t), t ≥ 0} with values that are non-negative, integer, and non-decreasing:
- N(t) ≥ 0.
- N(t) is an integer.
- 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 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.
References
[edit]- 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