Stochastic storage models and noise-induced phase transitions

The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes restrictions on the description of the phase transition problem where the system is to overcome some finite potential barrier, or systems with finite size where the fluctuations are comparable with the size of a system. We suggest a complementary stochastic description of physical systems based on the mathematical stochastic storage model with basic notions of random input and output into a system. It reproduces statistical distributions typical for noise-induced phase transitions (e.g. Verhulst model) for the simplest (up to linear) forms of the escape function. We consider a generalization of the stochastic model based on the series development of the kinetic potential. On the contrast to Gaussian processes in which the development in series over a small parameter characterizing the jump value is assumed [R.L. Stratonovich, Nonlinear Nonequilibrium Thermodynamics, Springer Series in Synergetics (Springer Verlag, 1994), Vol. 59], we propose a series expansion directly suitable for storage models and introduce the kinetic potential generalizing them. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006