A counting process is a stochastic process {N(t), t ≥ 0} with values that are non-negative, integer, and non-decreasing: 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.