Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion

We study pathwise properties and homeomorphic property with respect to the initial values for stochastic differential equations driven by G-Brownian motion. We first present a Burkholder-Davis-Gundy inequality and an extension of Itô's formula for the G-stochastic integrals. Some moment estimates and Hölder continuity of the G-stochastic integrals and the solutions of stochastic differential equations with Lipschitzian coefficients driven by G-Brownian motion are obtained. Homeomorphic property with respect to the initial values is also established.