Order-Preservation for Multidimensional Stochastic Functional Differential Equations with Jump

Xing Huang; Feng-Yu Wang

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arXiv · 1305.0991

Order-Preservation for Multidimensional Stochastic Functional Differential Equations with Jump

Xing Huang·Feng-Yu Wang

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Abstract

Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\R^d$ 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-dimesional equations and multidimensional equations without delay, and the necessity is new even in these special situations.

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Xing Huang, Feng-Yu Wang. 2014-01-21. Order-Preservation for Multidimensional Stochastic Functional Differential Equations with Jump. https://arxiv.org/abs/1305.0991

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