发表机构
School of Mathematics, Nanjing University; School of Mathematical Sciences, Dalian University of Technology（南京大学数学系; 大连理工大学数学科学学部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究由满足奇异摄动朗之万方程且具有缩放混合随机力的半鞅驱动的随机微分方程逼近。用扩散逼近法探索半鞅粗糙路径提升的极限，应用通用极限定理确定随机微分方程极限，还建立了混合随机力的迭代弱不变原理。
AI 中文摘要
我们研究由满足具有缩放混合随机力的奇异摄动朗之万方程的半鞅驱动的随机微分方程的逼近。通过扩散逼近方法，我们探索这个半鞅的粗糙路径提升的极限，并应用一个通用极限定理来识别随机微分方程的极限。一个结构上平行的证明也适用于为混合随机力建立一个迭代弱不变原理，这本身就是一个独立有趣的结果。我们发现，两个二级过程的极限都具有斯特拉托诺维奇形式的迭代积分加上与时间增量成比例的反对称部分的形式。
英文摘要
We investigate approximation of random differential equations driven by semimartingales satisfying a singularly perturbed Langevin equation with scaled mixing random force. By a diffusion approximation approach, we explore the limit of the rough path lift of this semimartingale, and a universal limit theorem is applied to identify the limit of random differential equation. A structurally parallel proof also applies to establish an iterated weak invariance principle for the mixing random force, which is itself an independent interesting result. We find that, the limit of both of the second-level processes, have the form of iterated integral of Stratonovich form plus an anti-symmetric part which is proportional to the time increment.
