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Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators

Author

Listed:
  • Falei Wang

    (Shandong University)

  • Guoqiang Zheng

    (Southeast University)

Abstract

The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar-valued backward stochastic differential equations driven by G-Brownian motion. In fact, when the generators are Lipschitz continuous in y and uniformly continuous in z, we construct the unique solution to such equations by a linearization technique and a monotone convergence argument. The comparison theorem and related nonlinear Feynman–Kac formula are stated as well.

Suggested Citation

  • Falei Wang & Guoqiang Zheng, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators," Journal of Theoretical Probability, Springer, vol. 34(2), pages 660-681, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00998-y
    DOI: 10.1007/s10959-020-00998-y
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    References listed on IDEAS

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