In this talk, we consider kinetic equations containing random
terms. The kinetic models contain a small parameter and it is well
known that, after scaling, when this parameter goes to zero the limit
problem is a diffusion equation in the PDE sense, ie a parabolic equation
of second order. A smooth noise is added, accounting for external perturbation.
It scales also with the small parameter. It is expected that the limit
equation is then a stochastic parabolic equation where the noise is in
Stratonovitch form.
Our aim is to justify in this way several SPDEs commonly used.
We first treat linear equations with multiplicative noise. Then show how
to extend the methods to nonlinear equations or to the more physical
case of a random forcing term.
The results have been obtained jointly with S. De Moor and J. Vovelle