A continuous time random walk model with multiple characteristic times

Abstract

In this paper we consider a continuous time random walk (CTRW) model with a decoupledjump pdf. Further, we consider an approximate jump length pdf; for the waiting time pdfwe do not use any approximation and we employ a function which depends onmultiple characteristic times given by a sum of exponential functions. This waitingtime pdf can reproduce power-law behavior for intermediate times. Using thisspecific waiting time probability density, we analyze the behavior of the secondmoment generated by the CTRW model. It is known that the waiting time pdfgiven by an exponential function generates a normal diffusion process, but for ourwaiting time pdf the second moment can give an anomalous diffusion processfor intermediate times, and the normal diffusion process is maintained for thelong-time limit. We note that systems which present subdiffusive behavior forintermediate times but reach normal diffusion at large times have been observed inbiology.