Limit theorems of continuous-time random walks with tails

摘要

We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Levy process in D([0,1]) with Mi-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0,1]) with J_1-topology.