Nonlinear fluctuations-induced rate equations for linear birth-death processes

Abstract

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.