Strong convergence of multi-scale stochastic differential equations with a full dependence

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-09-12 DOI:10.1016/j.spl.2024.110271

Qing Ji, Jicheng Liu

引用次数: 0

Abstract

This paper considers the strong convergence of multi-scale stochastic differential equations, where diffusion coefficient of the slow component depends on fast process. In this situation, it is well-known that strong convergence in the averaging principle does not hold in general.

We propose a new approximation equation, and prove that the order of strong convergence is

1 / 2

via the technique of Poisson equation. In particular, when diffusion coefficient of the slow component does not depend on fast process, the approximation equation is exactly the averaged equation. This provides us a new perspective to study the strong convergence of multi-scale stochastic differential equations with a full dependence.

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具有完全依赖性的多尺度随机微分方程的强收敛性

本文考虑了多尺度随机微分方程的强收敛问题，其中慢分量的扩散系数取决于快过程。我们提出了一个新的近似方程，并通过泊松方程技术证明了强收敛阶数为 1/2。我们提出了新的近似方程，并通过泊松方程技术证明了强收敛阶数为 1/2。特别是，当慢速分量的扩散系数不依赖于快速过程时，近似方程正是平均方程。这为我们研究具有完全依赖性的多尺度随机微分方程的强收敛性提供了一个新的视角。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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