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The problem on identification of a limit of an ordinary differential equationwith discontinuous drift that perturbed by a zero-noise is considered inmultidimensional case. This problem is a classical subject of stochasticanalysis. However the multidimensional case was poorly investigated. We assumethat the drift coefficient has a jump discontinuity along a hyperplane and isLipschitz continuous in the upper and lower half-spaces. It appears that thebehavior of the limit process depends on signs of the normal component of thedrift at the upper and lower half-spaces in a neighborhood of the hyperplane,all cases are considered.

On a Selection Problem for Small Noise Perturbation in Multidimensional Case