A Poisson process is a stochastic process. It counts the number of occurrences of an event leading up to a specified time. This is a counting process where the increments of time are independent of one another (the times do not overlap).
Definition
The counting process known as the Poisson process is defined as:
- N(0) = 0.
- N(t) has independent increments.
- The number of arrivals in any window of time follows a Poisson distribution.
Where N(t) is the total number of events that occur by time t.
