Homeomorphic Flows and Large Deviations for Stochastic Differential Equations Driven by aG-Brownian Motion

A Burkholder-Davis-Gundy inequality and an extension of Itô’s formula for the G-stochastic integrals are presented. 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 and large deviation principle for the stochastic differential equations are established. Reference