Abstract
Both Itô's stochastic differential equations, as well as equations driven by semimartingales, with non degenerate diffusion coefficient, are considered. Multidimensional pathwise uniqueness and non-contact property, as well as one dimensional homeomorphic property, of solutions, are studied under weak conditions on the coefficients. It will be shown that these properties hold for equations with non-locally Lipschitz diffusion matrix and only measurable drift
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