ASYMPTOTIC DISTRIBUTIONS OF CONTINUOUS-TIME RANDOM-WALKS - A PROBABILISTIC APPROACH

We provide a systematic analysis of the possible asymptotic distributi ons of one-dimensional continuous-time random walks (CTRWs) by applyin g the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previou s work concerning decoupled memory and Levy walks, we deal also with a rbitrary coupled memory and with jump densities asymmetric about its m ean, obtaining asymmetric Levy-stable limits. Suprisingly, it is found that in most cases coupled memory has no essential influence on the f orm of the limiting distribution. We discuss interesting properties of walks with an infinite mean waiting time between successive jumps.