Diagram representation for the stochastization of single-step processes

Abstract

Background. By the means of the method of stochastization of one-step processes we get the simplified mathematical model of the original stochastic system. We can explore these models by standard methods, as opposed to the original system. The process of stochastization depends on the type of the system under study. Purpose. We want to get a unified abstract formalism for stochastization of one-step processes. This formalism should be equivalent to the previously introduced. Methods. To unify the methods of construction of the master equation, we propose to use the diagram technique. Results. We get a diagram technique, which allows to unify getting master equation for the system under study. We demonstrate the equivalence of the occupation number representation and the state vectors representation by using a Verhulst model. Conclusions. We have suggested a convenient diagram formalism for unified construction of stochastic systems.