粗略微分方程的适度偏差

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-29 DOI:10.1112/blms.13097

Yuzuru Inahama, Yong Xu, Xiaoyu Yang

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摘要

小噪声问题对于所有类型的随机微分方程都相当重要。在本文中，我们重点研究由 Hurst 参数 H∈ ( 1 / 4 , 1 / 2 ]$ 的缩放分数布朗粗糙路径驱动的粗糙微分方程。 $H\in (1/4, 1/2]$ 。当尺度参数趋近于零时，我们证明了该方程的适度偏差原理。

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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Moderate deviations for rough differential equations

Small noise problems are quite important for all types of stochastic differential equations. In this paper, we focus on rough differential equations driven by scaled fractional Brownian rough path with Hurst parameter $H \in (1 / 4, 1 / 2]$ . We prove a moderate deviation principle for this equation as the scale parameter tends to zero.