On the equivalence of operator and combinatorial approaches for onestep random Markov processes

Abstract

Herein, for one-step random Markov processes the comparison of the operator and combinatorial methods based on the use of functional integrals is performed. With the combinatorial approach, the transition from the stochastic differential equation to the functional integral is used. This allows us to obtain the expression for the mean population size in terms of the functional integral. With the operator approach, the transition to the functional integral is performed via the creation and annihilation operators. It is shown that the mean values calculated using the functional integrals arising in the combinatorial and operator approaches coincide.