Geodesic
On the strong uniqueness of a solution to singular stochastic differential equations
Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 1-15.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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Olga V. Aryasova; Andrey Yu. Pilipenko. On the strong uniqueness of a solution to singular stochastic differential equations. Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 1-15. http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a0/

[1] A. S. Cherny, H.-J. Engelbert, Singular stochastic differential equations, Springer-Verlag, Berlin, 2005

[2] A. S. Cherny, “On the strong and weak solutions of stochastic differential equations governing bessel processes”, Stochastics and Stochastics Reports, 70:3 (2000), 213–219

[3] R. F. Bass, K. Burdzy, Z.-Q. Chen, “Pathwise uniqueness for a degenerate stochastic differential equation”, The Annals of Probability, 35:6 (2007), 2385–2418

[4] R. F. Bass, Z.-Q. Chen, “One-dimensional stochastic differential equations with singular and degenerate coefficients”, Sankhya: The Indian Journal of Statistics, 67 (2005), 19–45

[5] J. F. Le Gall, “Applications des temps local aux equations differentielles stochastiques unidimensionnelles”, Lecture Notes in Math., 986 (1983), 15–31

[6] I. V. Girsanov, “An example of non-uniqueness of the solution of the stochastic equation of K. Ito”, Theory of Probability and its Applications, 7 (1962), 325–331

[7] Springer-Verlag, Heidelberg-New York

[8] N. Ikeda, S. Watanabe, Stochastic differential equations and diffusion processes, Kodansha ltd., Tokyo, 1981

[9] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge Univ. Press, 1990

[10] H. P. McKean, Stochastic integrals, Academic Press, New York, London, 1969

[11] P. E. Protter, Stochastic integration and differential equations, Springer-Verlag, Berlin, 2004

[12] K. Ramanan, “Reflected diffusions defined via extended Skorokhod map”, Electronic journal of probability, 11 (2006), 934–992

[13] D. Revuz, M. Yor, Continuous martingales and Brownian motion, Springer-Verlag, Berlin, 1999

[14] D. W. Stroock, S. R. S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, Berlin, New York, 1979

[15] S. R. S. Varadhan, R. J. Williams, “Brownian motion in a wedge with oblique reflection”, Comm. Pure Appl. Math., 38 (1985), 405–443