  The aim of this paper is to evidence two points relative to Nonstandard
analysis (NSA): 1. In most applications of NSA to analysis, only elementary
facts and techniques of nonstandard calculus seems to be necessary. 2. The
advantages of a theory which includes infinitesimals rely more on the
possibility of making new models rather than in the proving techniques.
  These two points will be illustrated in the theory of Brownian motion which
can be considered as a classical model to test the power of the infinitesimal
approach. Starting from a naive idea of Brownian motion, we deduce the
Fokker-Plank equation in a simple and rigorous way. It is possible to keep
every things to a simple level since all the theory of stochastic differential
equations is treated as a hyperfinite theory and it is not translated in a
"standard model". The only standard object is the final one: the Fokker-Plank
equation.
