2024/03/07 by Shuzhen Yang, Wenqing Zhang, Yang, Shuzhen +1
Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2403.04324
openalex publication_date 2024/03/07 · openalex created_date 2024/03/09 · openalex updated_date 2026/08/01
In this study, we propose the sublinear expectation structure under countable state space. To describe an interesting "nonlinear randomized" trial, based on a convex compact domain, we introduce a family of probability measures under countable state space. Corresponding the sublinear expectation operator introduced by S. Peng, we consider the related notation under countable state space. Within the countable state framework, the sublinear expectation can be explicitly calculated by a novel repeated summation formula, and some interesting examples are given. Furthermore, we establish Monotone convergence theorem, Fatou's lemma and Dominated convergence theorem of sublinear expectation. Afterwards, we consider the independence under each probability measure, upon which we establish the sublinear law of large numbers and obtain the maximal distribution under sublinear expectation.