Extended foundations of stochastic prediction
  The basic purpose of this work was to suggest universal quantitative description of ergodic system intermediate bifurcation and obligatory conditions of this transition. Conditions for existence of phase state and first order phase transition were introduced in terms of energy balance for system volume unit. Extended Fokker - Plank equation with time dependent diffusion factor was formulated. It turned out that for ergodic system with fixed boundary quantized energy spectrum of phase stable states exists. Obtained results may be applied for prediction of ergodic system behavior. If isolation condition is satisfied, phase spectrum quantization allows selecting proper control parameters for system stabilization. Information about current system coarsened energy allows predicting of future stochastic system behavior on the basis of extended Fokker - Plank model. 
Sergey Kamenshchikov
nlin.CD nlin.AO