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Based on the weak existence and weak uniqueness, we study the pathwiseuniqueness of the solutions for a class of one-dimensional stochasticdifferential equations driven by pure jump processes. By using Tanaka's formulaand the local time technique, we show that there is no gap between the stronguniqueness and weak uniqueness when the coefficients of the Poisson randommeasures satisfy a suitable condition

Pathwise uniqueness for stochastic differential equations driven by pure jump processes