Probabilistic approximation of fully nonlinear second-order PIDEs with convergence rates for the universal robust limit theorem

Lianzi Jiang, Mingshang Hu and Gechun Liang

Stochastic Processes and their Applications, 2026, vol. 199, issue C

Abstract: This paper develops a probabilistic approximation scheme for a class of nonstandard, fully nonlinear second-order partial integro-differential equations (PIDEs) associated with nonlinear Lévy processes under Peng’s G-expectation framework. The PIDE features a supremum over a family of α-stable Lévy measures, possibly degenerate diffusion coefficients, and a non-separable uncertainty set, which places it outside the scope of existing numerical theories for PIDEs. We construct a recursive, piecewise-constant approximation of the viscosity solution and establish explicit error estimates for the scheme. As a key application, our results yield quantitative convergence rates for the universal robust limit theorem under sublinear expectations. This provides a unified treatment of Peng’s robust central limit theorem and law of large numbers, as well as the α-stable limit theorem of Bayraktar and Munk, together with explicit Berry-Esseen-type bounds.

Keywords: Partial-integral differential equation; Probabilistic approximation scheme; Universal robust limit theorem; Convergence rate; Error estimate; Sublinear expectation (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2026.104974

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