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<p>We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally Hölder continuous of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>. We show that the scheme converges in the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_2\)</EquationSource> </InlineEquation>-norm with a rate of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((1+\alpha )/2\)</EquationSource> </InlineEquation> over both finite intervals [0,&#xa0;<i>T</i>] and the infinite interval <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((0, +\infty )\)</EquationSource> </InlineEquation>, under certain growth conditions on the coefficients.</p>

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A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Thi-Huong Vu,
  • Hoang-Long Ngo,
  • Duc-Trong Luong,
  • Ngoc Khue Tran

摘要

We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally Hölder continuous of order \(\alpha \) . We show that the scheme converges in the \(L_2\) -norm with a rate of \((1+\alpha )/2\) over both finite intervals [0, T] and the infinite interval \((0, +\infty )\) , under certain growth conditions on the coefficients.