Scholarlink

<p>This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a blowup of moments of solutions and numerical solutions and thus affect the convergence of numerical methods. Wang et al. (2024, IMA J. Numer. Anal.) have analyzed weak convergence of one-step numerical schemes when solutions to SDEs have <i>infinitely many bounded moments</i>. Therein, some modified Euler schemes have been discussed about their weak convergence orders. In this work, we explore the effects of finitely many bounded moments on the weak convergence of a family of explicit one-step schemes. The schemes are based on approximations/modifications of terms in the Itô-Taylor expansion. We provide a systematic but simple way to establish weak convergence orders for these schemes. We present several numerical examples of these schemes and show their weak convergence orders.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Weak Error Analysis for Strong Approximation Schemes of SDEs with Super-Linear Coefficients II Finitely Many Bounded Moments and Higher-Order Schemes

  • 期刊论文

  • 发表日期：

    2025年10月15日

查看全文
  • Yuying Zhao,
  • Xiaojie Wang,
  • Zhongqiang Zhang

摘要

This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a blowup of moments of solutions and numerical solutions and thus affect the convergence of numerical methods. Wang et al. (2024, IMA J. Numer. Anal.) have analyzed weak convergence of one-step numerical schemes when solutions to SDEs have infinitely many bounded moments. Therein, some modified Euler schemes have been discussed about their weak convergence orders. In this work, we explore the effects of finitely many bounded moments on the weak convergence of a family of explicit one-step schemes. The schemes are based on approximations/modifications of terms in the Itô-Taylor expansion. We provide a systematic but simple way to establish weak convergence orders for these schemes. We present several numerical examples of these schemes and show their weak convergence orders.