Sublinear expectation structure under discrete state space

In this study, we develop a sublinear expectation structure on a discrete state space. To describe a nonlinear randomized trial, we construct a family of probability measures by a convex compact domain. Parallel to Peng’s sublinear expectation in continuous settings, we define its discrete concepts, which admits an explicit recursive summation calculation. Furthermore, we establish discrete analogs of the Monotone convergence theorem, Fatou’s lemma and the Dominated convergence theorem for the sublinear expectation. Based on a newly defined notion of independence, we derive a nonlinear law of large numbers and obtain the maximal distribution under sublinear expectation. • Parameterize a family of probability measures via a convex compact domain. • Establish an explicit computational framework for the sublinear expectation. • Convergence theorems of sublinear expectation are built on a discrete state space. • A novel proof of nonlinear law of large numbers in the discrete setting.