  A theoretical study is presented for the random aspect of an optical vortex
inherent in the nonlinear birefringent Kerr effect, which is called the optical
spin vortex. We start with the two-component nonlinear Schr\"{o}dinger
equation. The vortex is inherent in the spin texture caused by an anisotropy of
the dielectric tensor, for which the role of spin is played by the Stokes
vector (or pseudospin). The evolutional equation is derived for the vortex
center coordinate using the effective Lagrangian of the pseudospin field. This
is converted to the Langevin equation in the presence of the fluctuation
together with the dissipation. The corresponding Fokker-Planck equation is
derived and analytically solved for a particular form of the birefringence
inspired from the Faraday effect. The main consequence is that the relaxation
distance for the distribution function is expressed by the universal constant
in the Faraday effect and the size of optical vortex. The result would provide
a possible clue for future experimental study in polarization optics from a
stochastic aspect.
