  Presentation of the probability as an intrinsic property of the nature leads
researchers to switch from deterministic to stochastic description of the
phenomena. The procedure of stochastization of one-step process was formulated.
It allows to write down the master equation based on the type of of the kinetic
equations and assumptions about the nature of the process. The kinetics of the
interaction has recently attracted attention because it often occurs in the
physical, chemical, technical, biological, environmental, economic, and
sociological systems. However, there are no general methods for the direct
study of this equation. Leaving in the expansion terms up to the second order
we can get the Fokker-Planck equation, and thus the Langevin equation. It
should be clearly understood that these equations are approximate recording of
the master equation. However, this does not eliminate the need for the study of
the master equation. Moreover, the power series produced during the master
equation decomposition may be divergent (for example, in spatial models). This
makes it impossible to apply the classical perturbation theory. It is proposed
to use quantum field perturbation theory for the statistical systems (the
so-called Doi method). This work is a methodological material that describes
the principles of master equation solution based on quantum field perturbation
theory methods. The characteristic property of the work is that it is
intelligible for non-specialists in quantum field theory. As an example the
Verhulst model is used because of its simplicity and clarity (the first order
equation is independent of the spatial variables, however, contains
non-linearity). We show the full equivalence of the operator and combinatorial
methods of obtaining and study of the one-step process master equation.
