Asymptotic Distributions of the Continuous - TimeRandom

We provide a systematic analysis of the possible asymptotic distributions of one-dimensional continuous-time random walks (CTRWs) by applying the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previous works concerning decoupled memory and L evy walks, we deal also with arbitrary coupled memory and with jump densities asymmetric about its mean, obtaining asymmetric L evy-stable limits. Suprisingly, it is found that in most cases coupled memory has no essential innuence on the form of the limiting distribution. We discuss interesting properties of walks with an innnite mean waiting-time between successive jumps. Our results are summarized in Table I.