A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem

• DOI: 10.1016/j.jde.2024.03.013
• Publication Date: 2024-03-26T20:02:43Z
• Authors: Shuo Huang; Gechun Liang
• Keywords: Central limit theorem

We propose a monotone approximation scheme for class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization G-distributed random variables sublinear expectation space. The proposed is constructed recursively based on piecewise constant viscosity solution to G-equation. establish convergence and determine rate with an explicit error bound, using comparison principles both equation together mollification procedure. first application obtaining Peng's robust central limit theorem bound Berry-Esseen type. second its Black-Scholes-Barenblatt equation.