Velocity distribution for quasistable acceleration in the presence of multiplicative noise

Processes that are far both from equilibrium and from phase transition are studied. It is shown that a process with mean velocity that exhibits power-law growth in time can be analyzed using the Langevin equation with multiplicative noise. The solution to the corresponding Fokker-Planck equation is derived. Results of the numerical solution of the Langevin equation and simulation of the motion of particles in a billiard system with a time-dependent boundary are presented.