Kinetics of phase transitions with singular multiplicative noise

The behavior of the most probable values of the order parameter x and the a mplitude p of conjugate force fluctuations is studied for a stochastic syst em with a noise amplitude depending on x as \x\(a). It is shown that the ph ase half-plane x > 0 for the canonical pair x, p is divided into isolated r egions of large, intermediate, and small values of x. In the first region, the trajectories converge to values of x, p --> infinity as the time t --> infinity, and the probability of their realization is negligibly small. In the intermediate region, the configuration point tends to the attraction ce nter corresponding to a stationary ordered state. In the region x much less than 1, the trajectories converge to the point x = p = 0 for 0 < a < 1/2 a nd to x = 0, p --> infinity for 1/2 < a less than or equal to 1. In the for mer case, the probability of realization of trajectories is finite, while, in the latter case, it is negligibly small, and an absorbing state can be f ormed. (C) 2000 MAIK "Nauka/Interperiodica".