  We study the stochastic dynamics of a two-dimensional magnetic moment
embedded in a three-dimensional environment, described by means of the
stochastic Landau-Lifshitz-Gilbert (sLLG) equation. We define a covariant
generalization of this equation, valid in the "generalized Stratonovich
discretization prescription". We present a path integral formulation that
allows to compute any $n-$point correlation function, independently of the
stochastic calculus used. Using this formalism, we show the equivalence between
the cartesian formulation with vectorial noise, with the polar formulation with
just one scalar fluctuation term. In particular, we show that, for isotropic
fluctuations, the system is represented by an {\em additive stochastic
process}, despite of the multiplicative terms appearing in the original
formulation of the sLLG equation, but, for anisotropic fluctuations the noise
turns out to be truly multiplicative.
