Some properties for Itô processes driven by $G$-Brownian motion

Abstract

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.