Andrey Pilipenko (Kyiv)
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, 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.
