Abstract
In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function although the jump-diffusion coefficient could contain a delay function. Moreover, another example is established to show that the comparison theorem is not necessary to be true provided that the jump-diffusion term is non-increasing with respect to the delay variable.
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Bao, J., Yuan, C. Comparison Theorem for Stochastic Differential Delay Equations with Jumps. Acta Appl Math 116, 119 (2011). https://doi.org/10.1007/s10440-011-9633-7
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DOI: https://doi.org/10.1007/s10440-011-9633-7