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※
- 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