In this paper, we use partial differential equation (PDE) techniques and probabilistic approaches to study the lower capacity of the ball for the Itô process driven by $G$-Brownian motion ($G$-Itô process). In particular, the lower bound on the lower capacity of certain balls is obtained. As an application, we prove a strict comparison theorem in $G$-expectation framework.
"Some properties for Itô processes driven by $G$-Brownian motion." Electron. Commun. Probab. 22 1 - 10, 2017. https://doi.org/10.1214/17-ECP78