Unified description of internal fluctuations and external white poisson noise

Abstract

A theory for a unified description of internal fluctuations and external noise is presented. External noise is introduced by random parameters in a master equation by using a Poisson white noise. The theory predicts the existence of a coupling of the two types of fluctuations leading to “crossed-fluctuation” contributions. The effect of the system size in a type of transition induced by external noise in the thermodynamic limit is discussed by considering a birth-death process with source term and fluctuations in the annihilation parameter.