O. Aryasova, A. Pilipenko, “On exponential decay of a distance between solutions of an SDE with non-regular drift”, Theory Stoch. Process., 2019, Volume 24(40), Issue 2,Pages <nobr>1

On exponential decay of a distance between solutions of an SDE with non-regular drift

O. Aryasova^a, A. Pilipenko^b

^a Institute of Geophysics, National Academy of Sciences of Ukraine, 32 Palladin ave., 03142, Kyiv, Ukraine; National Technical University of Ukraine “Igor Sikorsky Kyiv Politechnic Institute”, Kyiv, Ukraine
^b Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska str., 01601, Kyiv, Ukraine; National Technical University of Ukraine “Igor Sikorsky Kyiv Politechnic Institute”, Kyiv, Ukraine

Abstract: 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.

Keywords: SDE with discontinuous coefficients, Long-time behavior of solutions.

MSC: 60H10, 60H99

Language: English