Pathwise properties and homeomorphic flows for stochastic differential equations driven by -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.