Counting process


A counting process is a stochastic process with values that are non-negative, integer, and non-decreasing:
  1. N ≥ 0.
  2. N is an integer.
  3. If s ≤ t then N ≤ N.
If s < t, then N − N 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.