论文标题
$ l^\ infty $ drift的SDE的零噪声限制
The zero-noise limit of SDEs with $L^\infty$ drift
论文作者
论文摘要
我们研究具有不连续右侧的自主，一维的普通微分方程的零噪声极限。尽管确定性方程可能具有无限的解决方案，但在相当普遍的条件下，我们表明，随机扰动的溶液的序列会收敛于确定性方程的经典解决方案上的唯一分布。我们提供了几种计算此限制分布的工具。
We study the zero-noise limit for autonomous, one-dimensional ordinary differential equations with discontinuous right-hand sides. Although the deterministic equation might have infinitely many solutions, we show, under rather general conditions, that the sequence of stochastically perturbed solutions converges to a unique distribution on classical solutions of the deterministic equation. We provide several tools for computing this limit distribution.
