{"title":"Numerical schemes for radial Dunkl processes","authors":"Hoang-Long Ngo, Dai Taguchi","doi":"10.1093/imanum/draf005","DOIUrl":null,"url":null,"abstract":"We consider the numerical approximation for a class of radial Dunkl processes corresponding to arbitrary (reduced) root systems in $\\mathbb{R}^{d}$. This class contains well-known processes such as Bessel processes, Dyson’s Brownian motions and square root of Wishart processes. We propose some semi-implicit and truncated Euler–Maruyama schemes for radial Dunkl processes and study their convergence rate with respect to the $L^{p}$-sup norm.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imanum/draf005","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
We consider the numerical approximation for a class of radial Dunkl processes corresponding to arbitrary (reduced) root systems in $\mathbb{R}^{d}$. This class contains well-known processes such as Bessel processes, Dyson’s Brownian motions and square root of Wishart processes. We propose some semi-implicit and truncated Euler–Maruyama schemes for radial Dunkl processes and study their convergence rate with respect to the $L^{p}$-sup norm.
期刊介绍:
The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.