Counting process

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

i. N(t)≥ 0.
ii. N(t) has to be an integer.
iii. if s<t then N(s)≤ N(t).
iv. assuming s<t, N(t)-N(s) is the number of events occurred during the interval(s,t].

References

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