{"title":"A novel second order scheme with one step for forward backward stochastic differential equations","authors":"Qiang Han, Shihao Lan, Quanxin Zhu","doi":"arxiv-2409.07118","DOIUrl":null,"url":null,"abstract":"In this paper, we present a novel explicit second order scheme with one step\nfor solving the forward backward stochastic differential equations, with the\nCrank-Nicolson method as a specific instance within our proposed framework. We\nfirst present a rigorous stability result, followed by precise error estimates\nthat confirm the proposed novel scheme achieves second-order convergence. The\ntheoretical results for the proposed methods are supported by numerical\nexperiments.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present a novel explicit second order scheme with one step
for solving the forward backward stochastic differential equations, with the
Crank-Nicolson method as a specific instance within our proposed framework. We
first present a rigorous stability result, followed by precise error estimates
that confirm the proposed novel scheme achieves second-order convergence. The
theoretical results for the proposed methods are supported by numerical
experiments.