Work

How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme

Year: 2025

Type: article

Abstract: We propose an effective explicit numerical scheme for simulating solutions of stochastic differential equations with confining superlinear drift terms, driven by multiplicative heavy-tailed Lévy noise. The scheme is designed to prevent explosion and accurately capture all finite moments of the solutions. In the purely Gaussian case, it correctly reproduces moments of sub-Gaussian tails of the solutions. This method is particularly well-suited for approximating statistical moments and other probabilistic characteristics of Lévy flights in steep potential landscapes.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0301147

Authors: I. Pavlyukevich, O. Aryasova, A. Chechkin, O. Kulyk

Institutions: Friedrich Schiller University Jena, Max Planck Institute of Microstructure Physics, Wrocław University of Science and Technology

Language: English

Topic: stochastic dynamics and bifurcation

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung

Awards: G2810335498, G5293465434