On exponential decay of a distance between solutions of an SDE with non-regular drift
O. Aryasova, A. PilipenkoTheory of Stochastic Processes
Vol.24 (40), no.2, 2019, pp.1-13
We consider a multidimensional stochastic differential equation with a Gaussian noise and a drift vector having a jump discontinuity along a hyperplane. The large time behavior of the distance between two solutions starting from different points is studied. We find a sufficient condition for the exponential decay of the distance if the drift does not satisfy a dissipative condition on a given hyperplane.