Backward stochastic differential equations with a uniformly continuous generator and related gg-expectation

In this paper, we will study a class of backward stochastic differential equations (BSDEs for short), for which the generator (coefficient) g(t,y,z)g(t,y,z) is Lipschitz continuous with respect to yy and uniformly continuous with respect to zz. We establish several properties for such BSDEs, including comparison and converse comparison theorems, a representation theorem for gg and a continuous dependence theorem. Then we introduce a new class of gg-expectation based on such backward stochastic differential equations, and discuss its properties.