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On the comparison theorem for multi-dimensional G-SDEs

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  • Luo, Peng
  • Wang, Falei

Abstract

In this paper, we establish a viability result for stochastic differential equations (SDEs) driven by a multi-dimensional G-Brownian motion. Then we obtain a sufficient and necessary condition for comparison theorem of multi-dimensional G-SDEs by an equivalent criterion of viability condition for G-SDEs.

Suggested Citation

  • Luo, Peng & Wang, Falei, 2015. "On the comparison theorem for multi-dimensional G-SDEs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 38-44.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:38-44
    DOI: 10.1016/j.spl.2014.09.010
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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. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    3. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    4. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    5. Luo, Peng & Wang, Falei, 2014. "Stochastic differential equations driven by G-Brownian motion and ordinary differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3869-3885.
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    Cited by:

    1. Yang, Fen-Fen & Yuan, Chenggui, 2022. "Comparison theorem for neutral stochastic functional differential equations driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Rahman Ullah & Faiz Faizullah & Quanxin Zhu, 2024. "The Convergence and Boundedness of Solutions to SFDEs with the G-Framework," Mathematics, MDPI, vol. 12(2), pages 1-12, January.

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