Counting process

A counting process is a stochastic process {N(t), t ≥ 0} that possesses the following properties:

1. N(t) ≥ 0.
2. N(t) is an integer.
3. 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 ]. One example is a Poisson process.

References

• Ross, S.M. (1995) Stochastic Processes. Wiley. ISBN 978-0471120629