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Theory of Stochastic Processes, 2019, Volume 24(40), Issue 2, Pages 1–13 (Mi thsp302)  
On exponential decay of a distance between solutions of an SDE with non-regular drift

O. Aryasovaa, A. Pilipenkob

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
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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.
Funding agency Grant number
Alexander von Humboldt-Stiftung
The research is partially supported by the Alexander von Humboldt Foundation (Project “Singular diffusions: analytic and stochastic approaches”)
Document Type: Article
MSC: 60H10, 60H99
Language: English
Citation: O. Aryasova, A. Pilipenko, “On exponential decay of a distance between solutions of an SDE with non-regular drift”, Theory Stoch. Process., 24(40):2 (2019), 1–13
Citation in format AMSBIB
\Bibitem{AryPil19}
\by O.~Aryasova, A.~Pilipenko
\paper On exponential decay of a distance between solutions of an SDE with non-regular drift
\jour Theory Stoch. Process.
\yr 2019
\vol 24(40)
\issue 2
\pages 1--13
\mathnet{http://mi.mathnet.ru/thsp302}
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