Numerical Schemes for Backward Stochastic Differential Equations Driven by G-Brownian motion
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We design a class of numerical schemes for backward stochastic differential equation driven by G-Brownian motion (G-BSDE), which is related to a fully nonlinear PDE. Based on Peng's central limit theorem, we employ the CLT method to approximate G-distributed. Rigorous stability and convergence analysis are also carried out. It is shown that the θ-scheme admits a half order convergence rate in the general case. In particular, for the case of θ_1∈[0,1] and θ_2=0, the scheme can reach first-order in the deterministic case. Several numerical tests are given to support our theoretical results.
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