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Stochastic differential equations driven by G-Brownian motion and ordinary differential equations

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  • Luo, Peng
  • Wang, Falei

Abstract

In this paper, we show that the integration of a stochastic differential equation driven by G-Brownian motion (G-SDE for short) in R can be reduced to the integration of an ordinary differential equation (ODE for short) parameterized by a variable in (Ω,F). By this result, we obtain a comparison theorem forG-SDEs and its applications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:11:p:3869-3885
    DOI: 10.1016/j.spa.2014.07.004
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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.
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    Cited by:

    1. Hu, Mingshang & Ji, Xiaojun & Liu, Guomin, 2021. "On the strong Markov property for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 417-453.
    2. 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).
    3. Luo, Peng & Wang, Falei, 2015. "On the comparison theorem for multi-dimensional G-SDEs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 38-44.

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