2015/10/04 by Andrey Pilipenko, Pilipenko, Andrey, Frank Proske +1
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1510.00966
openalex publication_date 2015/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem on identification of a limit of an ordinary differential equation\nwith discontinuous drift that perturbed by a zero-noise is considered in\nmultidimensional case. This problem is a classical subject of stochastic\nanalysis. However the multidimensional case was poorly investigated. We assume\nthat the drift coefficient has a jump discontinuity along a hyperplane and is\nLipschitz continuous in the upper and lower half-spaces. It appears that the\nbehavior of the limit process depends on signs of the normal component of the\ndrift at the upper and lower half-spaces in a neighborhood of the hyperplane,\nall cases are considered.\n