AI 中文总结
研究由分数布朗运动驱动的随机微分方程，通过改写方程为快慢系统及分解快分量研究小质量极限与收敛速率，在正则条件下用弱收敛方法研究带小乘性噪声方程的大、中偏差原理。
AI 中文摘要
本文讨论了一类由带加性噪声的分数布朗运动驱动的随机微分方程，受斯莫卢霍夫斯基-克莱默斯近似启发的一种近似的有效性。通过将此类方程改写为快慢系统形式并将快分量分解为三部分，研究了这些方程的小质量极限并推导了相应收敛速率。此外，在一定正则性条件下，通过弱收敛方法研究了一类带小乘性噪声的分数布朗运动驱动的随机微分方程的大偏差和中偏差原理。
英文摘要
In this paper, we discuss the validity of an approximation inspired by the Smoluchowski-Kramers approximation for a class of stochastic differential equations driven by fractional Brownian motion with additive noise. By rewriting such equations in the form of slow-fast systems and decomposing the fast component into three parts, we investigate the small mass limit of these equations and derive the corresponding convergence rates. Furthermore, under certain regularity conditions, we study the large and moderate deviation principles for a class of stochastic differential equations driven by fractional Brownian motion with small multiplicative noise via the weak convergence approach.
