Correlated continuous time random walk with time averaged waiting time

•The correlated continuous time random walk is considered.•Time averaged waiting time is introduced.•The mean square displacements, generalized Einstein relation and asymptotic behavior of this process are discussed.•Ergodicity breaking for this process is found by computing time averaged mean square displacements.

In this paper, we study the dynamics of a correlated continuous time random walk with time averaged waiting time. The mean square displacement (MSD) shows this process is subdiffusive and generalized Einstein relation holds. We also get the asymptotic behavior of the probability density function (PDF) of this process is stretched Gaussian. At last, by computing the time averaged MSD, we find ergodicity breaking occurs in this process.