路径唯一性下具有跳跃的随机微分方程解的欧拉逼近与稳定性

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE

Finance and Stochastics Pub Date : 2022-05-12 DOI:10.1080/17442508.2022.2071107

Kaoutar Nasroallah, Y. Ouknine

{"title":"路径唯一性下具有跳跃的随机微分方程解的欧拉逼近与稳定性","authors":"Kaoutar Nasroallah, Y. Ouknine","doi":"10.1080/17442508.2022.2071107","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a stochastic differential equation with jumps for which pathwise uniqueness hold. We establish a fundamental mean square convergence theorem for the Euler approximation scheme. We provide some results on strong stability with respect to small perturbations of the initial conditions, and we study the convergence of Picard approximations.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"77 1","pages":"266 - 302"},"PeriodicalIF":1.1000,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Euler approximation and stability of the solution to stochastic differential equations with jumps under pathwise uniqueness\",\"authors\":\"Kaoutar Nasroallah, Y. Ouknine\",\"doi\":\"10.1080/17442508.2022.2071107\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a stochastic differential equation with jumps for which pathwise uniqueness hold. We establish a fundamental mean square convergence theorem for the Euler approximation scheme. We provide some results on strong stability with respect to small perturbations of the initial conditions, and we study the convergence of Picard approximations.\",\"PeriodicalId\":50447,\"journal\":{\"name\":\"Finance and Stochastics\",\"volume\":\"77 1\",\"pages\":\"266 - 302\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finance and Stochastics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2022.2071107\",\"RegionNum\":2,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance and Stochastics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1080/17442508.2022.2071107","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}

引用次数: 2

摘要

本文研究了一类具有跳跃的随机微分方程，该方程具有路径唯一性。建立了欧拉近似格式的均方收敛基本定理。我们给出了关于初始条件的小扰动的强稳定性的一些结果，并研究了皮卡德近似的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Euler approximation and stability of the solution to stochastic differential equations with jumps under pathwise uniqueness

In this paper, we consider a stochastic differential equation with jumps for which pathwise uniqueness hold. We establish a fundamental mean square convergence theorem for the Euler approximation scheme. We provide some results on strong stability with respect to small perturbations of the initial conditions, and we study the convergence of Picard approximations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.