How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909993828089856 |
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| author | Pavlyukevich, Ilya Aryasova, Olga Chechkin, Alexei Kulyk, Oleksii |
| author_facet | Pavlyukevich, Ilya Aryasova, Olga Chechkin, Alexei Kulyk, Oleksii |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme Pavlyukevich, Ilya Aryasova, Olga Chechkin, Alexei Kulyk, Oleksii Computational Physics Statistical Mechanics Probability 65C30, 60H35 G.3; G.1.7; J.2; I.6 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. |
| title | How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme |
| topic | Computational Physics Statistical Mechanics Probability 65C30, 60H35 G.3; G.1.7; J.2; I.6 |
| url | https://arxiv.org/abs/2508.07339 |