ABSTRACT

The Feynman-Kac formula establishes the probabilistic representation of solutions to PDEs, linking the convergence of numerical schemes for PDEs to limit theorems in probability theory. In this talk, we extend this idea beyond linear settings to nonlinear settings such as sublinear expectations (also known as Peng’s G-expectations) and convex expectations. We establish convergence rates for central limit theorems, laws of large numbers, and alpha-stable limit theorems under sublinear/convex expectations. Our approach employs the convergence analysis of viscosity solutions for corresponding fully nonlinear PDEs, focusing on the Barles-Souganidis monotone scheme analysis and the related techniques developed by Krylov, Barles, and Jakobsen. The talk is based on a series of joint works with Jonas Blessing, Mingshang Hu, Shuo Huang, Lianzi Jiang, Michael Kupper, and Shige Peng.