Geodesic
On exponential decay of a distance between solutions of an SDE with non-regular drift
Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 1-13

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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. 
@article{THSP_2019_24_2_a0,
     author = {O. Aryasova and A. Pilipenko},
     title = {On exponential decay of a distance between solutions of an {SDE} with non-regular drift},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {1--13},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a0/}
}
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O. Aryasova; A. Pilipenko. On exponential decay of a distance between solutions of an SDE with non-regular drift. Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 1-13. http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a0/