Scholarlink

<p>An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations. We establish the strong convergence rate of the standard Euler–Maruyama method under the global Lipschitz condition. The theoretical analysis is then extended to the truncated Euler–Maruyama method, proving its strong convergence under relaxed Khasminskii-type conditions. Under suitable conditions, the strong convergence orders of both numerical schemes are shown to be close to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha /2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is the parameter of the time-change process. These results are significantly different from existing works using random step sizes, which typically preserve the classical convergence order of 1/2. Numerical simulations are provided to demonstrate the theoretical findings.</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

Parameter-Related strong convergence rates of Euler-type methods for time-changed stochastic differential equations

  • 期刊论文

  • 发表日期：

    2026年7月29日

查看全文
  • Ruchun Zuo

摘要

An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations. We establish the strong convergence rate of the standard Euler–Maruyama method under the global Lipschitz condition. The theoretical analysis is then extended to the truncated Euler–Maruyama method, proving its strong convergence under relaxed Khasminskii-type conditions. Under suitable conditions, the strong convergence orders of both numerical schemes are shown to be close to \(\alpha /2\) α / 2 , where \(\alpha \in (0,1)\) α ∈ ( 0 , 1 ) is the parameter of the time-change process. These results are significantly different from existing works using random step sizes, which typically preserve the classical convergence order of 1/2. Numerical simulations are provided to demonstrate the theoretical findings.