  The consistent and computationally efficient stochastic statistical approach
(SSA) is suggested to study kinetics of nucleation and evolution of nano-sized
precipitates in alloys. An important parameter of the theory is the size of
locally equilibrated regions at the nucleation stage which is estimated using
the "maximum thermodynamic gain" principle suggested.
  For several realistic models of iron-copper alloys studied, the results of
the SSA-based simulations of precipitation kinetics agree well with the kinetic
Monte Carlo simulation results for all main characteristics of microstructure.
The approach developed is also used to study kinetics of nucleation and changes
in microstructural evolution under variations of temperature or concentration.
