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Theory of Stochastic Processes, 2011, Volume 17(33), Issue 2, Pages 1–15 (Mi thsp48)  
On the strong uniqueness of a solution to singular stochastic differential equations

Olga V. Aryasovaa, Andrey Yu. Pilipenkob

a 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
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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.
Funding agency Grant number
State Fund for Fundamental Researches (Ukraine) F40.1/023
This work was partially supported by the State fund for fundamental researches of Ukraine and the Russian foundation for basic research under project F40.1/023.
Bibliographic databases:
Document Type: Article
MSC: 60J65, 60H10
Language: English
Citation: Olga V. Aryasova, Andrey Yu. Pilipenko, “On the strong uniqueness of a solution to singular stochastic differential equations”, Theory Stoch. Process., 17(33):2 (2011), 1–15
Citation in format AMSBIB
\Bibitem{AryPil11}
\by Olga~V.~Aryasova, Andrey~Yu.~Pilipenko
\paper On the strong uniqueness of a solution to singular stochastic differential equations
\jour Theory Stoch. Process.
\yr 2011
\vol 17(33)
\issue 2
\pages 1--15
\mathnet{http://mi.mathnet.ru/thsp48}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2934555}
\zmath{https://zbmath.org/?q=an:1249.60177}
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