Limit theorems of continuous-time random walks with tails

Abstract

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 Lévy process in D([0, 1]) with M₁-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J₁-topology.

Keywords

Weak convergence / J₁-topology / M₁-topology / stable Lévy process

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