论文标题
通过高斯粗糙路径驱动的粗糙微分方程的噪声正规化
Regularization by noise for rough differential equations driven by Gaussian rough paths
论文作者
论文摘要
我们考虑由高斯几何粗糙路径驱动的漂移的粗糙微分方程。在粗糙路径上的自然条件下，即非确定性和扩散系数上均匀的椭圆度条件，我们证明了方程式良好的规则漂移的路径良好。对于$ h> \ frac14 $的分数布朗运动$ b^h $，我们证明漂移可能为$κ> 0 $hölder连续连续，并以$κ> \ frac32- \ frac1- \ frac1 {2h} $限制。高斯粗糙路径的方程和Malliavin演算的流动转换用于实现这种结果。
We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion $B^H$ for $H>\frac14$, we prove that the drift may be taken to be $κ>0$ Hölder continuous and bounded for $κ>\frac32 - \frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achieve such a result.
