论文标题
动力学SDE的噪声正规化强的正规化
Strong regularization by noise for kinetic SDEs
论文作者
论文摘要
在本文中，我们证明了由退化的扩散驱动的随机微分方程系统的良好体系，可以满足弱型Hörmander条件，假设Hölder规律性假设对漂移系数。该框架包括动力学SDES的随机Langevin系统。允许速度成分的漂移系数连续$α$-Hölder，而无需限制索引$α$，这可以是$] 0,1 [$中的任何正数。由于这些差异系统的确定性对应物没有很好地拟合，因此可以将此结果视为一种被称为正规化噪声的现象。
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type Hörmander condition, assuming Hölder regularity assumptions on the drift coefficient. This framework encompasses, as particular cases, stochastic Langevin systems of kinetic SDEs. The drift coefficient of the velocity component is allowed to be $α$-Hölder continuous without any restriction on the index $α$, which can be any positive number in $]0,1[$. As the deterministic counterparts of these differential systems are not well-posed, this result can be viewed as a phenomenon known as regularization by noise.
