On a Selection Problem for Small Noise Perturbation in Multidimensional Case

Andrey Pilipenko; Frank Norbert Proske

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arXiv · 1510.00966

On a Selection Problem for Small Noise Perturbation in Multidimensional Case

Andrey Pilipenko·Frank Norbert Proske

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Abstract

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.

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Andrey Pilipenko, Frank Norbert Proske. 2015-10-04. On a Selection Problem for Small Noise Perturbation in Multidimensional Case. https://arxiv.org/abs/1510.00966

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