  We study the stochastic behavior of a set of chaotic vortex loops appeared in
imperfect Bose gas. Dynamics of Bose-gas is supposed to obey Gross-Pitaevskii
equation with additional noise satisfying fluctuation-dissipation relation. The
corresponding Fokker-Planck equation for probability functional has solution
${\cal P}(\{{\psi}({\bf r})\})={\cal N}\exp (-H\{{\psi}({\bf r)}\} /T),$ where
$H\{{\psi}({\bf r})\} $ is the Ginzburg-Landau free energy. Considering vortex
filaments as topological defects of field ${\psi}({\bf r})$ we derive a
Langevin-type equation of motion of the line with the correspondingly
transformed stirring force. The respective Fokker-Planck equation for
probability functional ${\cal P}(\{{\bf s}(\xi)\})$ in vortex loop
configuration space is shown to have a solution in the form of ${\cal P}(\{{\bf
s}(\xi)\})={\cal N}\exp (-H\{{\bf s}\} /T),$ where ${\cal N}$ is the
normalizing factor and $H\{{\bf s}\} $ is energy of vortex line configurations.
Analyzing this result we discuss possible reasons for destruction of the
thermodynamic equilibrium and follow the mechanisms of transition to the
turbulent state
