Poisson point process

A Poisson Process is a Stochastic Process which counts the number of occurrences of an event leading up to a specified time. This is referred to as a counting process where the increments of time are independent from one another (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 interval of length 𝜏 > 0 follows a Poisson distribution.

Where N(t) is the total number of events that occur by time t.