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Strong convergence of compensated split-step theta methods for SDEs with jumps under monotone condition

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  • Yue, Chao

Abstract

This paper is concerned with strong convergence of the compensated split-step theta (CSST) method for autonomous stochastic differential equations (SDEs) with jumps under weaker conditions. More precisely, the diffusion coefficient and the drift coefficient are both locally Lipschitz and the jump-diffusion coefficient is globally Lipschitz, while they all satisfy the monotone condition. It is proved that the CSST method is strongly convergent of order 12. Finally, the obtained results are supported by numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:72-83
    DOI: 10.1016/j.amc.2018.04.002
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    References listed on IDEAS

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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
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    Cited by:

    1. 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).

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