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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\u00e9vy flights in steep potential landscapes.<\/jats:p>","DOI":"10.1063\/5.0301147","type":"journal-article","created":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T14:06:57Z","timestamp":1766412417000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["How to simulate L\u00e9vy flights in a steep potential: An explicit splitting numerical scheme"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2059-0912","authenticated-orcid":false,"given":"I.","family":"Pavlyukevich","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Friedrich Schiller University Jena 1 , Inselplatz 5, 07743 Jena,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5870-8349","authenticated-orcid":false,"given":"O.","family":"Aryasova","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Friedrich Schiller University Jena 1 , Inselplatz 5, 07743 Jena,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3803-1174","authenticated-orcid":false,"given":"A.","family":"Chechkin","sequence":"additional","affiliation":[{"name":"Max Planck Institute of Microstructure Physics 2 , Weinberg 2, 06120 Halle,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9371-6862","authenticated-orcid":false,"given":"O.","family":"Kulyk","sequence":"additional","affiliation":[{"name":"Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology 3 , Wybrze\u017ae Wyspia\u0144skiego 27, 50-370 Wroclaw,","place":["Poland"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,12,22]]},"reference":[{"key":"2025122209065217400_c1","doi-asserted-by":"publisher","first-page":"134709","DOI":"10.1016\/j.physd.2025.134709","article-title":"Escape by jumps and diffusion by \u03b1-stable noise across the barrier in a double well potential","volume":"479","year":"2025","journal-title":"Phys. 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