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A counting process is a stochastic process {N, t ≥ 0} with values that are non-negative, integer, and non-decreasing:
If s < t, then N − N is the number of events occurred during the interval. 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.
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