On a Selection Problem for Small Noise Perturbation in Multidimensional Case

02.12.2015, 8:15-9:45  –  Golm, Haus 9, Raum 1.10
Forschungsseminar Wahrscheinlichkeitstheorie

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.