BRICS 2021 — Venue SH | Invited Talk by Prof. Bruce Watson
Channel: BRICS Mathematics Conference 2021
Date: 2021-12-07

Title: Discrete time martingales, mixingales and mixing processes in Riesz spaces
Speaker: Bruce Watson, University of the Witwatersrand

Abstract: Mixingales are stochastic processes which combine the concepts of martingales and mixing sequences. McLeish introduced the term mixingale in 1974. We generalize the concept of a mixingale to the measure-free Riesz space setting. This generalizes all of the L_p; 1 ⩽ p ⩽ ∞ variants. We also generalize the concept of uniform integrability to the Riesz space setting and prove that a weak law of large numbers holds for Riesz space mixingales. Connections are also made with discrete time martingales and mixing processes in both the L_p space and the Riesz space settings will be discussed. This talk is based on joint work with Wen-Chi Kuo and various other coauthors.