Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories

TL;DR

This paper discusses Fogedby's Langevin equation-based model for continuous time random walks and demonstrates its effectiveness for numerically generating sample paths of these stochastic processes.

Contribution

It provides a detailed analysis of Fogedby's model and introduces a robust numerical method for simulating continuous time random walk trajectories.

Findings

Effective numerical generation of CTRW sample paths

Validation of Fogedby's Langevin-based model

Enhanced understanding of CTRW dynamics

Abstract

Continuous time random walks have been developed as a straightforward generalisation of classical random walk processes. Some 10 years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin equations [H. C. Fogedby, Phys. Rev. E 50 (1994)]. The present work is devoted to a detailed discussion of Fogedby's model and presents its application for the robust numerical generation of sample paths of continuous time random walk processes.