Stochastic Motion Under G-Framework: I. Nelson Stochastic Derivatives

Abstract

In this article we take the initial step in the study of kinematics of stochastic motion under the sublinear expectation approach, (the so called G-framework). We compute, in this article, the stochastic forward/backward derivatives/drifts of some G-diffusion processes, and calculate the current and osmotic velocities. While the G-framework that we use creates a few technical difficulties, it also rewards us with nice extensions of results corresponding to the linear expectation case.