The paper focuses on the analysis of mean-square contractivity of the numerical dynamics arising from the application of \(\theta \) -Maruyama methods to stochastic differential equations (SDEs) with linear affine drift and diffusion coefficients. We prove that the numerical deviation between two distinct solutions of the SDE is monotonically non-increasing under the same stepsize restrictions needed for mean-square stability or holds unconditionally for certain values of \(\theta \) . A selection of numerical experiments complements the theoretical investigation.

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

Mean-Square Monotonicity Analysis of  \(\theta \) -Maruyama Methods

  • Helena Biščević,
  • Raffaele D’Ambrosio

摘要

The paper focuses on the analysis of mean-square contractivity of the numerical dynamics arising from the application of \(\theta \) -Maruyama methods to stochastic differential equations (SDEs) with linear affine drift and diffusion coefficients. We prove that the numerical deviation between two distinct solutions of the SDE is monotonically non-increasing under the same stepsize restrictions needed for mean-square stability or holds unconditionally for certain values of \(\theta \) . A selection of numerical experiments complements the theoretical investigation.