Study On G-Diffusion Processes

In this paper, we study G-Diffusion processes. First of all, we give the def-initions about two types of transition operators (Pt)t>o and (Pt)t>o associated with G-Diffusion processes. Then, we discuss some properties about them, such as con-tractibility, sublinear property, semigroup property, continuity and Feller property. On this basis, we further define infinitesimal generator, excessive function and resolvent operator under the G-Expectation. In addition, we provide some properties about them. At last, we present the specific representation about Pt and the corresponding properties in some special cases.