  In this article, 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 the first step toward the mathematical
understanding of thermal effects on a ferromagnet. In a first part, we present
the stochastic model and prove that the associated stochastic differential
equation is well defined. The second part is dedicated to the study of the long
time behaviour of the magnetic moment and in the third part we prove that the
stochastic perturbation induces a non reversibility phenomenon. Last, we
illustrate these results through numerical simulations of our stochastic model.
  The main results presented in this article are the rate of convergence of the
magnetization toward the unique stable equilibrium of the deterministic model.
The second result is a sharp estimate of the hysteresis phenomenon induced by
the stochastic perturbation (remember that with no perturbation, the magnetic
moment remains constant).
