  When nano-magnets are coupled to random external sources, their magnetization
becomes a random variable, whose properties are defined by an induced
probability density, that can be reconstructed from its moments, using the
Langevin equation, for mapping the noise to the dynamical degrees of freedom.
When the spin dynamics is discretized in time, a general
fluctuation-dissipation theorem, valid for non-Markovian noise, can be
established, even when zero modes are present. We discuss the subtleties that
arise, when Gilbert damping is present and the mapping between noise and spin
degrees of freedom is non--linear.
