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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), revised 24 Feb 2020 (this version, v3), latest version 26 Mar 2024 (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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