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This page contains a short introductory lecture on the Poisson Process. In this lecture we construct the Poisson Process, a continuous time stochastic process that models the occurrence of rare independent events. In more mathematical terms, the process has jumps of hight 1 at each time t>0 at which a random event is observed, i.e. it is a random monotonously increasing function function N(t) with values in non-negative integers (see picture). The waiting times between events are independent and exponentially distributed.

This process has wide ranging applications from modelling the arrival of customers at a shop to the time instances at which a decay within a radioactive material is observed.