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arXiv · 1707.01019

Mixingales on Riesz spaces

Wen-Chi Kuo·Jessica Joy Vardy·Bruce Alastair Watson
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Abstract

A mixingale is a stochastic process which combines properties of martingales and mixing sequences. McLeish introduced the term mixingale at the $4^{th}$ Conference on Stochastic Processes and Application, at York University, Toronto, 1974, in the context of $L^2$. In this paper we generalize the concept of a mixingale to the measure-free Riesz space setting (this generalizes all of the $L^p, 1\le p\le \infty$ variants) and prove that a weak law of large numbers holds for Riesz space mixingales. In the process we also generalize the concept of uniform integrability to the Riesz space setting.

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BibTeXRIS

Wen-Chi Kuo, Jessica Joy Vardy, Bruce Alastair Watson. 2017-07-04. Mixingales on Riesz spaces. https://doi.org/10.1016/j.jmaa.2013.02.001

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