Stochastic Order Based On Sublinear Expectation

In this paper,we mainly consider the property of stochastic order in the framework of sublinear expectations space (Ω,H,E). Firstly, we give the generalized definition of ordinary stochastic order and convex order based on the sublinear expectations space; Secondly, we prove that ordinary stochastic order have closure for monotonically increas-ing functiont φ1 (x), φ2 (x, y); Finally, we provide equivalent conditions between convex order and increasing convex order, and prove their several properties. We finally achieve generalization of the classical situation in the sublinear expectations space.