Order preservation for multidimensional stochastic functional differential equations with jumps

Abstract

Sufficient and necessary conditions are presented for the order preservation of stochastic functional differential equations on \({\mathbb{R}^d}\) 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.

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Correspondence to Feng-Yu Wang.

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Supported in part by Lab. Math. Com. Sys. and NNSFC (11131003).

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Huang, X., Wang, FY. Order preservation for multidimensional stochastic functional differential equations with jumps. J. Evol. Equ. 14, 445–460 (2014). https://doi.org/10.1007/s00028-014-0222-x

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Mathematics Subject Classification

  • 60J75
  • 47G20
  • 60G52

Keywords

  • Order preservation
  • comparison theorem
  • stochastic functional differential equation