  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 [Stratonovich R.L.,
Nonlinear Nonequilibrium Thermodynamics, Springer Series in Synergetics,
vol.59, Springer Verlag, 1994], we propose a series expansion directly suitable
for storage models and introduce the kinetic potential generalizing them.
