Generalized master equations for continuous-time random walks

Abstract

An equivalence is established between generalized master equations and continuous-time random walks by means of an explicit relationship betweenψ(t), which is the pausing time distribution in the theory of continuous-time random walks, andφ(t), which represents the memory in the kernel of a generalized master equation. The result of Bedeaux, Lakatos-Lindenburg, and Shuler concerning the equivalence of the Markovian master equation and a continuous-time random walk with an exponential distribution forψ(t) is recovered immediately. Some explicit examples ofφ(t) andψ(t) are also presented, including one which leads to the equation of telegraphy.