On a selection problem for small noise perturbation in the multidimensional case
On a selection problem for small noise perturbation in the multidimensional case
复制标题
多维情况下小噪声扰动的选择问题
作者：
A. Pilipenko;F. Proske
在多维情况下，研究了零噪声扰动下具有不连续漂移的常微分方程的极限辨识问题。这个问题是随机分析的经典课题，参见[6,29,11,20]。然而，对多维病例的调查很少。我们假设漂移系数沿超平面具有跳变不连续，并且在上下半空间中是Lipschitz连续的。似乎极限过程的行为取决于在超平面的邻域上半空间和下半空间漂移的法向分量的符号，所有情况都被考虑。
The problem on identification of a limit of an ordinary differential equation with discontinuous drift that perturbed by a zero-noise is considered in multidimensional case. This problem is a classical subject of stochastic analysis, see, for example, [6, 29, 11, 20]. However the multidimensional case was poorly investigated. We assume that the drift coefficient has a jump discontinuity along a hyperplane and is Lipschitz continuous in the upper and lower half-spaces. It appears that the behavior of the limit process depends on signs of the normal component of the drift at the upper and lower half-spaces in a neighborhood of the hyperplane, all cases are considered.