无噪声正则化
Noiseless regularisation by noise
摘要：
我们分析了一般连续可加扰动对常微分方程适定性的影响。这里的普遍性是从普遍性的意义上理解的。这使我们能够讨论这些问题的设置，我们不必承诺任何限制性假设的统计性质的扰动。主要结果是，一般的连续扰动呈现柯西问题适定的任意不规则向量场。因此，我们通过噪声“无概率”建立正则化。
英文摘要：
We analyse the effect of a generic continuous additive perturbation to the well-posedness of ordinary differential equations. Genericity here is understood in the sense of prevalence. This allows us to discuss these problems in a setting where we do not have to commit ourselves to any restrictive assumption on the statistical properties of the perturbation. The main result is that a generic continuous perturbation renders the Cauchy problem well-posed for arbitrarily irregular vector fields. Therefore we establish regularisation by noise "without probability".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
