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$$L^p$$ L p -Error Estimates for Numerical Schemes for Solving Certain Kinds of Mean-Field Backward Stochastic Differential Equations

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  • Wei Zhang

    (Beijing University of Technology)

  • Hui Min

    (Beijing University of Technology)

Abstract

In this paper, we propose two numerical methods for solving certain kinds of mean-field backward stochastic differential equations: first-order numerical scheme and Crank–Nicolson numerical scheme. Then, we study $$L^p$$ L p -error estimates for the proposed schemes. We prove that the two schemes are of second-order convergence in solving for $$Y_t$$ Y t in $$L^p$$ L p norm; the first-order scheme is of first-order convergence and the Crank–Nicolson scheme is of second-order convergence in solving $$Z_t$$ Z t in $$L^p$$ L p norm.

Suggested Citation

  • Wei Zhang & Hui Min, 2023. "$$L^p$$ L p -Error Estimates for Numerical Schemes for Solving Certain Kinds of Mean-Field Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(2), pages 762-778, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01184-y
    DOI: 10.1007/s10959-022-01184-y
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    References listed on IDEAS

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    1. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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