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Projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition

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  • Li, Min
  • Huang, Chengming

Abstract

In this paper, we investigate a projected Euler-Maruyama method for stochastic delay differential equations with variable delay under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalize the idea of C-stability and B-consistency given by Beyn et al. (2016) to the case with delay. Moreover, the method is proved to be convergent with order one-half in a succinct way. Finally, some numerical examples are included to support our theoretical results.

Suggested Citation

  • Li, Min & Huang, Chengming, 2020. "Projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307258
    DOI: 10.1016/j.amc.2019.124733
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    References listed on IDEAS

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    1. Tan, Li & Yuan, Chenggui, 2018. "Strong convergence of a tamed theta scheme for NSDDEs with one-sided Lipschitz drift," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 607-623.
    2. Li, Xiuping & Cao, Wanrong, 2015. "On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 373-381.
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    Cited by:

    1. Zhenyu Wang & Qiang Ma & Xiaohua Ding, 2020. "Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    2. Zhao, Jingjun & Yi, Yulian & Xu, Yang, 2021. "Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 398(C).

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