  In this paper, we introduce a Markov process whose unique invariant
distribution is the Curie-Weiss model of self-organized criticality (SOC) we
designed in arXiv:1301.6911. In the Gaussian case, we prove rigorously that it
is a dynamical model of SOC: the fluctuations of the sum $S_{n}(\,\cdot\,)$ of
the process evolve in a time scale of order $\sqrt{n}$ and in a space scale of
order $n^{3/4}$ and the limiting process is the solution of a "critical"
stochastic differential equation.
