Comparison Theorem for Stochastic Differential Delay Equations with Jumps

2011/02/10 by Jianhai Bao, Chenggui Yuan, Bao, Jianhai +1
Computer Science · Economics, Econometrics and Finance · Engineering · #37H10 #39A11 #FOS: Mathematics #Neural Networks Stability and Synchronization #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1102.2165

openalex publication_date 2011/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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