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Sufficient and necessary conditions are presented for the order preservation of stochastic functional differential equations on $${\mathbb{R}^d}$$ R d with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency of the conditions extends and improves some known comparison theorems derived recently for one-dimensional equations and multidimensional equations without delay, and the necessity is new even in these special situations.
Journal of Evolution Equations – Springer Journals
Published: Jun 1, 2014
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