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

2019/04/15 by Huang, Shuo, Liang, Gechun · 2 citations
#60F05 #60H30 #65M15 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1904.07184

Abstract

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 Berry-Esseen type. The second application is an approximation scheme with its convergence rate for the Black-Scholes-Barenblatt equation.

Cited by

• Probabilistic approximation of fully nonlinear second-order PIDEs with convergence rates for the universal robust limit theorem
• Limit theorems under nonlinear expectations dominated by sublinear expectations

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