2024/11/05 by Wen Huang, Huang, Wen, Chunlin Liu +5
Computer Science · Engineering · #60F17 #60G65 #FOS: Mathematics #Fault Detection and Control Systems #Neural Networks and Applications #Primary 37A25 #Probability (math.PR) #Target Tracking and Data Fusion in Sensor Networks #secondary 28A12
paper · pdf · doi:10.48550/arxiv.2411.03512
openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear expectation systems are ergodic, we derive stronger results. Furthermore, we relax the conditions for the law of large numbers and the strong law of large numbers under sublinear expectations from independent and identical distribution to α-mixing. These results can be applied to a class of stochastic differential equations driven by G-Brownian motion (i.e., G-SDEs), such as G-Ornstein-Uhlenbeck processes. As byproducts, we also obtain a series of applications for classical ergodic theory and capacity theory.