论文标题
通过加性噪声正规化乘法SDE
Regularization of multiplicative SDEs through additive noise
论文作者
论文摘要
我们研究了某些添加剂连续扰动对具有乘法分数布朗运动（FBM）的正则作用。传统上，施加了对漂移和扩散系数的要求，以确保SDE的存在和独特性。我们表明，即使在漂移和扩散系数都是分布的，因此，适当的扰动恢复了产生方程的流动的存在，独特性和规律性，从而将正则化程序扩展到噪声的乘法sdes情况。 我们的方法依赖于Catellier和Gubinelli开发的非线性年轻形式主义的结合，以及Hairer和Li最近获得的随机平均估计值。
We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the program of regularization by noise to the case of multiplicative SDEs. Our method relies on a combination of the non-linear Young formalism developed by Catellier and Gubinelli, and stochastic averaging estimates recently obtained by Hairer and Li.
