Gauge theory of self-similar system

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.