  In this work, we are interested in the behaviour of a single ferromagnetic
mono--domain particle submitted to an external field with a stochastic
perturbation. This model is a step toward the mathematical understanding of
thermal effects on ferromagnets. In a first part, we discuss modelling issues
and propose several ways to integrate a random noise in the deterministic
model. Then, among all these approaches, we focus on the more natural one and
study its long time behaviour. We prove that the system converges to the unique
stable equilibrium of the deterministic model and make precise the L^p rate of
the convergence. Finally, we illustrate the theoretical results by numerical
simulations.
