论文标题
通过粗糙，年轻和普通微分方程中的乘法噪声通过乘法的途径正则化
Path-by-path regularisation through multiplicative noise in rough, Young, and ordinary differential equations
论文作者
论文摘要
考虑了通过乘法分数布朗动作扰动的微分方程。根据赫斯特参数$ h $的值，结果方程式被视为ode，yde或rde。在所有三个制度中，我们通过证明最强大的良好性具有不规则漂移的态度：强烈的存在和逐步唯一性，通过噪声现象进行了正则化。在年轻而光滑的制度中，$ h> 1/2 $在漂移系数上的条件是最佳的，因为它与添加剂案例已知的那个[CG16，GER22]一致。在（1/3,1/2）$中的粗糙制度$ h \中，我们假设良好的良好的良好的漂移规律性，而对于分布漂移，我们会获得薄弱的存在。
Differential equations perturbed by multiplicative fractional Brownian motions are considered. Depending on the value of the Hurst parameter $H$, the resulting equation is pathwise viewed as an ODE, YDE, or RDE. In all three regimes we show regularisation by noise phenomena by proving the strongest kind of well-posedness with irregular drift: strong existence and path-by-path uniqueness. In the Young and smooth regime $H>1/2$ the condition on the drift coefficient is optimal in the sense that it agrees with the one known for the additive case [CG16, Ger22]. In the rough regime $H\in(1/3,1/2)$ we assume positive but arbitrarily small drift regularity for strong well-posedness, while for distributional drift we obtain weak existence.
