Martingales, mixingales and mixing processes in Riesz spaces
Mixingales are stochastic processes which combine the concepts of martingales and mixing sequences.
McLeish introduced the term mixingale at the 4th Conference of Stochastic Processes
and Applications, at York University, Toronto in 1974. We generalize the concept of a mixingale
to the measure-free Riesz space setting. This generalizes all of the Lp; 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. The connections between martingales, mixingales and mixing processes in both the Lp space and the Riesz space settings will be discussed.
This talk is based on joint work with Coenraad Labuschagne, Jessica Vardy and Bruce Watson.