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Donsker-Type Theorem for Numerical Schemes of Backward Stochastic Differential Equations

Author

Listed:
  • Yi Guo

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China)

  • Naiqi Liu

    (School of Mathematics, Shandong University, Jinan 250100, China)

Abstract

This article studies the theoretical properties of the numerical scheme for backward stochastic differential equations, extending the relevant results of Briand et al. with more general assumptions. To be more precise, the Brown motion will be approximated using the sum of a sequence of martingale differences or a sequence of i.i.d. Gaussian variables instead of the i.i.d. Bernoulli sequence. We cope with an adaptation problem of Y n by defining a new process Y ^ n ; then, we can obtain the Donsker-type theorem for numerical solutions using a similar method to Briand et al.

Suggested Citation

  • Yi Guo & Naiqi Liu, 2025. "Donsker-Type Theorem for Numerical Schemes of Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 13(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:684-:d:1595050
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Coquet, François & Mackevicius, Vigirdas & Mémin, Jean, 1998. "Stability in of martingales and backward equations under discretization of filtration," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 235-248, July.
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