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Large deviations for stochastic differential equations driven by G-Brownian motion

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  • Gao, Fuqing
  • Jiang, Hui

Abstract

A joint large deviation principle for G-Brownian motion and its quadratic variation process is presented. The rate function is not a quadratic form due to quadratic variation uncertainty. A large deviation principle for stochastic differential equations driven by G-Brownian motion is also established.

Suggested Citation

  • Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:11:p:2212-2240
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    References listed on IDEAS

    as
    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. Baldi, P. & Ben Arous, G. & Kerkyacharian, G., 1992. "Large deviations and the Strassen theorem in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 171-180, August.
    3. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
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    Cited by:

    1. 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.
    2. Blessing, Jonas & Kupper, Michael & Nendel, Max, 2023. "Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups," Center for Mathematical Economics Working Papers 680, Center for Mathematical Economics, Bielefeld University.
    3. Ibrahim Dakaou & Abdoulaye Soumana Hima, 2021. "Large Deviations for Backward Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 34(2), pages 499-521, June.
    4. 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.
    5. Xu, Mingzhou & Cheng, Kun, 2022. "How small are the increments of G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 186(C).
    6. Xu, Jie, 2023. "A deviation inequality for increment of a G-Brownian motion under G-expectation and applications," Statistics & Probability Letters, Elsevier, vol. 198(C).
    7. Soumana Hima, Abdoulaye & Dakaou, Ibrahim, 2023. "Large deviation principle for Reflected Stochastic Differential Equations driven by G-Brownian motion in non-convex domains," Statistics & Probability Letters, Elsevier, vol. 193(C).

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