Functional convergence of continuous-time random walks with continuous paths

Magdziarz, M. & Żebrowski, P. ORCID: https://orcid.org/0000-0001-5283-8049 (2022). Functional convergence of continuous-time random walks with continuous paths. Communications in Contemporary Mathematics 10.1142/S0219199721501066.

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Abstract

Continuous-time random walks (CTRWs) are generic models of anomalous diffusion and fractional dynamics in statistical physics. They are typically defined in the way that their trajectories are discontinuous step functions. In this paper, we propose alternative definition of CTRWs with continuous trajectories. We also give the scaling limit theorem for sequence of such random walks. In general case this result requires the use of strong Skorohod M1 topology instead of Skorohod J1 topology, which is usually used in limit theorems for ordinary CTRW processes. We also give additional conditions under which convergence of sequence of considered random walks holds in the J1 topology.

Item Type: Article
Uncontrolled Keywords: Continuous-time random walk; anomalous diffusion; fractional dynamics; limit theorem; scaling limit; functional convergence; Skorohod topology
Research Programs: Advancing Systems Analysis (ASA)
Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM)
Depositing User: Luke Kirwan
Date Deposited: 29 Mar 2022 14:22
Last Modified: 29 Mar 2022 14:22
URI: http://pure.iiasa.ac.at/17936

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