Introduction

The branching Brownian motions (BBM)  is part of family of processes in the probability theory. It is the combination of two processes: a Brownian motion and a Galton-Watson process. The BBM has many applications in biology, physics and finance.
In this document, we will first give the mathematical meaning of the BBM and state some results.  Then, we will purpose a simulation of the BBM. Finally, we will give some applications of this process.
As stated earlier, the BBM combines two simple processes which are : Brownian motions and Galton-Watson processes. Let us first define the Brownian motion. 

Brownian motions