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We study a class of stochastic differential equations driven by semimartingale with non-Lipschitz coefficients. New sufficient conditions on the strong uniqueness and the nonexplosion are derived for d -dimensional stochastic differential equations on R d ( d > 2 ) with non-Lipschitz coefficients, which extend and improve Fei’s results.

Nonexplosion and Pathwise Uniqueness of Stochastic Differential Equation Driven by Continuous Semimartingale with Non-Lipschitz Coefficients