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The object of the present paper is to find new sufficient conditions for theexistence of unique strong solutions to a class of (time-inhomogeneous)stochastic differential equations with random, non-Lipschitzian coefficients.We give an example to show that our conditions are indeed weaker than thoserelevant conditions existing in the literature. We also derive momentestimations for the maximum process of the solution. Finally, we present asufficient condition to ensure the non confluence property of the solution oftime-homogeneous SDE which, in one dimension, is nothing but stochasticmonotone property of the solution.

New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients