Convergence Rates of Robust Limit Theorems under Nonlinear Expectations: A Monotone Scheme Analysis
Professor Gechun Liang
Date & Time
15 Nov 2023 (Wed) | 05:30 PM - 06:30 PM
Venue
Online via Zoom
Zoom link:
https://cityu.zoom.us/j/97267902838?pwd=VWJKTnJXdFdFT2hNVVBxL0N4SXhvUT09
Zoom ID 972 6790 2838
Passcode: 699108
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.