Mixing inequalities in Riesz spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Kuo, Wen-Chi¹  Rogans, Michael J.²  Watson, Bruce A.³ 

[1] Univ Witwatersrand, Sch Computat & Appl Math, Private Bag 3, ZA-2050 Po Wits, South Africa

[2] Univ Witwatersrand, Sch Stat & Actuarial Sci, Private Bag 3, ZA-2050 Po Wits, South Africa

[3] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Po Wits, South Africa

关键词: Riesz spaces;    Vector lattices;    Mixing processes;    Dependent processes;    Conditional expectation operators;   

DOI  :  10.1016/j.jmaa.2017.07.035

来源: Elsevier

【 摘 要 】

Various topics in stochastic processes have been considered in the abstract setting of Riesz spaces, for example martingales, martingale convergence, ergodic theory, AMARTS, Markov processes and mixingales. Here we continue the relaxation of conditional independence begun in the study of mixingales and study mixing processes. The two mixing coefficients which will be considered are the alpha (strong) and phi (uniform) mixing coefficients. We conclude with mixing inequalities for these types of processes. In order to facilitate this development, the study of generalized L-1 and L-infinity spaces begun by Kuo, Labuschagne and Watson will be extended. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free