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Doss-Lenglart [5] gave a strong comparison theorem under the C 2-continuity of diffusion coefficient
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Yamada, T., Ogura, Y. On the strong comparison theorems for solutions of stochastic differential equations. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 3–19 (1981). https://doi.org/10.1007/BF00531971
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DOI: https://doi.org/10.1007/BF00531971