How to simulate L\'evy flights in a steep potential: An explicit splitting numerical scheme

Ilya Pavlyukevich; Olga Aryasova; Alexei Chechkin; Oleksii Kulyk

doi:10.1063/5.0301147

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arXiv · 2508.07339

How to simulate L\'evy flights in a steep potential: An explicit splitting numerical scheme

Ilya Pavlyukevich·Olga Aryasova·Alexei Chechkin·Oleksii Kulyk

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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 L\'evy 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 L\'evy flights in steep potential landscapes.

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Ilya Pavlyukevich, Olga Aryasova, Alexei Chechkin, Oleksii Kulyk. 2025-08-10. How to simulate L\'evy flights in a steep potential: An explicit splitting numerical scheme. https://doi.org/10.1063/5.0301147

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