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On the averaging principle for stochastic differential equations driven by G-Lévy process

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  • Yuan, Mingxia
  • Wang, Bingjun
  • Yang, Zhiyan

Abstract

In this paper, we investigate the averaging principle for stochastic differential equation driven by G-Lévy process. By the BDG inequality for G-stochastic calculus with respect to G-Lévy process, we show that the solution of averaged stochastic differential equation driven by G-Lévy process converges to that of the standard one, under non-Lipschitz condition, in the mean square sense and also in capacity. An example is presented to illustrate the efficiency of the obtained results.

Suggested Citation

  • Yuan, Mingxia & Wang, Bingjun & Yang, Zhiyan, 2023. "On the averaging principle for stochastic differential equations driven by G-Lévy process," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715223000135
    DOI: 10.1016/j.spl.2023.109789
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    References listed on IDEAS

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    1. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    2. Ren, Liying, 2013. "On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1301-1310.
    3. Hu, Mingshang & Wang, Falei, 2021. "Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 139-171.
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