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Girsanov Theorem for G-Brownian Motion: The Degenerate Case

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  • Guomin Liu

    (Fudan University)

Abstract

In this paper, we prove the Girsanov theorem for G-Brownian motion without the non-degenerate condition. The proof is based on the perturbation method in the nonlinear setting by constructing a product space of the G-expectation space and a linear space that contains a standard Brownian motion. The estimates for exponential martingales of G-Brownian motion are important for our arguments.

Suggested Citation

  • Guomin Liu, 2021. "Girsanov Theorem for G-Brownian Motion: The Degenerate Case," Journal of Theoretical Probability, Springer, vol. 34(1), pages 125-140, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-020-00997-z
    DOI: 10.1007/s10959-020-00997-z
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    References listed on IDEAS

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    1. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
    2. Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
    3. 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.
    4. 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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