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Compensated projected Euler-Maruyama method for stochastic differential equations with superlinear jumps

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  • Li, Min
  • Huang, Chengming
  • Chen, Ziheng

Abstract

In this paper, we present and analyze a compensated projected Euler-Maruyama method for stochastic differential equations with jumps. A mean square convergence result is derived under a coupled condition. This condition and some reasonable assumptions admit that the jump and diffusion coefficients can be superlinear. Moreover, since the Poisson increment has different moment properties from the Brownian increment, some new techniques are developed for convergence analysis. Finally, some numerical experiments are carried out to confirm the theoretical results.

Suggested Citation

  • Li, Min & Huang, Chengming & Chen, Ziheng, 2021. "Compensated projected Euler-Maruyama method for stochastic differential equations with superlinear jumps," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    • Handle: RePEc:eee:apmaco:v:393:y:2021:i:c:s009630032030713x
    DOI: 10.1016/j.amc.2020.125760
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    References listed on IDEAS

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    1. Yue, Chao, 2019. "Strong convergence of compensated split-step theta methods for SDEs with jumps under monotone condition," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 72-83.
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    Cited by:

    1. Yang Li & Yaolei Wang & Taitao Feng & Yifei Xin, 2021. "A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps," Mathematics, MDPI, vol. 9(3), pages 1-14, January.

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