A stochastic process {N(t), t>=0} is said to be a CountingProcess if N(t) represents the total number of "events" that have occured up to time t. 

It must satisfy 
(i) N(t) >= 0 
(ii) N(t) is integer valued.
(iii) If  s < t , then N(s) <= N(t)
(iv) For s < t, N(t) - N(s) equals the number of events that have occurred in the interval (s,t]

A CountingProcess is said to possess ''independent increments'' if the nembers of events that occur in disjoint time intervals are independent.

A CountingProcess is said to possess ''stationary increments '' if the distribution of the number of events that occur in any interval of time depends only on the length of the time interval.



SeeAlso PoissonProcess