大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

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

Gechun Liang (University of Warwick)

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

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第115回

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

Gechun Liang (University of Warwick)

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