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

Wei Zhang () and Hui Min ()
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Wei Zhang: Beijing University of Technology
Hui Min: Beijing University of Technology

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 762-778

Abstract: 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.

Keywords: Mean-field backward stochastic differential equations; Numerical scheme; $$L^p$$ L p -error estimate; 60H35; 60H10; 65C20; 65C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01184-y

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