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Mathematics > Probability
Title: A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem
(Submitted on 15 Apr 2019 (v1), last revised 26 Mar 2024 (this version, v4))
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.
Submission history
From: Gechun Liang [view email][v1] Mon, 15 Apr 2019 16:59:14 GMT (24kb)
[v2] Mon, 22 Apr 2019 12:37:55 GMT (25kb)
[v3] Mon, 24 Feb 2020 16:26:53 GMT (31kb)
[v4] Tue, 26 Mar 2024 21:55:47 GMT (32kb)
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