Backward stochastic differential equations with a uniformly continuous generator and related g-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) is Lipschitz continuous with respect to y and uniformly continuous with respect to z. We establish several properties for such BSDEs, including comparison and converse comparison theorems, a representation theorem for g and a continuous dependence theorem. Then we introduce a new class of g-expectation based on such backward stochastic differential equations, and discuss its properties.