On the strong uniqueness of a solution to singular stochastic differential equations

Olga V. Aryasova^a, Andrey Yu. Pilipenko<sup>b

a</sup> Institute of Geophysics, National Academy of Sciences of Ukraine, Palladin pr. 32, 03680, Kiev-142, Ukraine
^b Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska str. 3, 01601, Kiev, Ukraine

Abstract: We prove the existence and uniqueness of a strong solution for an SDE on a semi-axis with singularities at the point $0$. The result obtained yields, for example, the strong uniqueness of non-negative solutions to SDEs governing Bessel processes.

Keywords: Singular SDE, strong uniqueness, martingale problem, local time.

MSC: 60J65, 60H10

Language: English

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