  We analyzed the stochastic behavior of systems controlled by autocatalytic
reaction A+X -> X+X, X+X -> A+X, X -> B provided that the distribution of
reacting particles in the system volume is uniform, i.e. the point model of
reaction kinetics introduced in arXiv:cond-mat/0404402 can be applied. Assuming
the number of substrate particles A to be kept constant by a suitable
reservoir, we derived the forward Kolmogorov equation for the probability of
finding n=0,1,... autocatalytic particles X in the system at a given time
moment. We have shown that the stochastic model results in an equation for the
mean value of autocatalytic particles X which differs strongly from the kinetic
rate equation. It has been found that not only the law of the mass action is
violated but also the bifurcation point is disappeared in the well-known
diagram of X particle- vs. A particle-concentration. Therefore, speculations
about the role of autocatalytic reactions in processes of the "natural
selection" can be hardly supported.
