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On the strong Markov property for stochastic differential equations driven by G-Brownian motion

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  • Hu, Mingshang
  • Ji, Xiaojun
  • Liu, Guomin

Abstract

The objective of this paper is to study the strong Markov property for the stochastic differential equations driven by G-Brownian motion (G-SDEs for short). We first extend the deterministic-time conditional G-expectation to optional times. The strong Markov property for G-SDEs is then obtained by Kolmogorov’s criterion for tightness. In particular, for any given optional time τ and G-Brownian motion B, the reflection principle for B holds and (Bτ+t−Bτ)t≥0 is still a G-Brownian motion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:131:y:2021:i:c:p:417-453
    DOI: 10.1016/j.spa.2020.09.015
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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. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    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. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    5. 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.
    6. 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.
    7. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    8. 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. 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.

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