4. Poisson process

A fundamental property of Brownian motion is the Markov property, i.e. that the prediction of the state of the process at time t, conditional on knowledge of its past up to time s $\left(s\le t\right)$ , depends only on the state of the system at time s.

Many processes other than Brownian motion, whose general form can be described, satisfy this property; they are called Markov processes. They model many everyday phenomena, in particular discontinuous ones, such as the evolution of a population of particles undergoing shocks (billiard balls, gas molecules), the evolution of the occupancy rate of a line in a telephone exchange, the evolution of a queue facing one or more servers.

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