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

The objective of the present paper is to find new sufficient conditions for the existence 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 those relevant conditions existing in the literature. We also derive moment estimations for the maximum process of the solution. Finally, we present a sufficient condition to ensure the non confluence property of the solution of time-homogeneous SDE which, in one dimension, is nothing but stochastic monotone property of the solution.