Counting process

A counting process is a stochastic process $\backslash \{N(t),\; t\backslash geq0\backslash \}$ with values that are non-negative, integer, and non-decreasing:

1. $N(t)\backslash geq0.$
2. $N(t)$ is an integer.
3. If $s\backslash leq\; t$ then $N(s)\backslash leq\; N(t).$

If

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.