Simulation of the continuous-time random walk using subordination schemes

TL;DR

This paper introduces an algorithm based on subordination schemes to simulate continuous-time random walks, accurately capturing key statistical properties and behaviors over long time scales across various applications.

Contribution

The work presents a novel algorithm that efficiently simulates continuous-time random walks using subordinate formulas, validated against standard observables and applicable in multiple scientific fields.

Findings

Algorithm accurately reproduces positional fluctuations

Matches theoretical predictions for mean and variance

Successfully simulates breakthrough curves with bias

Abstract

The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate data of the continuous time random walk in the long time limit. The algorithm has been validated using commonly employed observables, such as typical fluctuations of the positional distribution, rare fluctuations, the mean and the variance of the position, and breakthrough curves with time-dependent bias, demonstrating a perfect match.