{"title":"具有赫尔德漂移的莱维过程驱动的 SDE 的 Euler-Maruyama 方案","authors":"Yanfang Li, Guohuan Zhao","doi":"10.1016/j.spl.2024.110220","DOIUrl":null,"url":null,"abstract":"<div><p>This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler–Maruyama scheme. We derive the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-error for a broad range of driven noises, including all nondegenerate <span><math><mi>α</mi></math></span>-stable processes (<span><math><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></mrow></math></span>).</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Euler–Maruyama scheme for SDE driven by Lévy process with Hölder drift\",\"authors\":\"Yanfang Li, Guohuan Zhao\",\"doi\":\"10.1016/j.spl.2024.110220\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler–Maruyama scheme. We derive the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-error for a broad range of driven noises, including all nondegenerate <span><math><mi>α</mi></math></span>-stable processes (<span><math><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></mrow></math></span>).</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167715224001895\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224001895","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Euler–Maruyama scheme for SDE driven by Lévy process with Hölder drift
This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler–Maruyama scheme. We derive the -error for a broad range of driven noises, including all nondegenerate -stable processes ().
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