  On the basis of a dilatation invariant Lagrangian, governed equations are
determined for probability density and gauge potential of the non-stationary
self-similar stochastic system. It is shown that an automodel regime is
observed at small time interval determined by the Tsallis' parameter $q>1$. An
exponential falling down happens at large time where the dilatation parameter
and the partial scale tend to constant values.
