Mixingales on Riesz spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Kuo, Wen-Chi¹  Vardy, Jessica Joy²  Watson, Bruce Alastair² 

[1] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 P O Wits, South Africa

[2] Univ Witwatersrand, Sch Math, ZA-2050 P O Wits, South Africa

关键词: Riesz spaces;    Vector lattices;    Mixingales;    Martingales;    Independence;    Dependent processes;    Laws of large numbers;   

DOI  :  10.1016/j.jmaa.2013.02.001

来源: Elsevier

【 摘 要 】

A mixingale is a stochastic process which combines properties of martingales and mixing sequences. McLeish introduced the term mixingale at the 4th 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 <= p <= infinity 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. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free