  Numerical simulation of stochastic dynamics of vortex filaments under action
of random (Langevin) force is fulfilled. Calculations are performed on base of
the full Biot--Savart law for different intensities of the Langevin force. A
new algorithm, which is based on consideration of crossing lines, is used for
vortex reconnection procedure. After some transient period the vortex tangle
develops into the stationary state characterizing by the developed fluctuations
of various physical quantities, such as total length, energy etc. We tested
this state to learn whether or not it the thermodynamic equilibrium is reached.
With the use of a special treatment, so called method of weighted histograms,
we process the distribution energy of the vortex system. The results obtained
demonstrate that the thermodynamical equilibrium state with the temperature
obtained from the fluctuation dissipation theorem is really reached.
PACS-numbers: 67.40.Vs 98.80.Cq 7.37.+q
