Riesz空间中的近时相依性
Near-Epoch Dependence in Riesz Spaces
摘要：
在过去的15年里，Grobler、Kuo、Labuschagne、Stoica、Troitsky和Watson等学者将随机过程的研究抽象到巴拿赫格和向量格上，并对此进行了大量的研究。相比之下，混合过程很少受到关注。特别地，在{ \sc W.- C. Kuo，J. J. Vardy，文学士Watson，} Riesz空间上的Mixingales，{ \em J. Math. Anal. Appl.}，\textbf{402}（2013），第731-738页。在{ \sc W.- C. Kuo，M. J. Rogans，文学士Watson，} Riesz空间中的混合不等式，{ \em J. Math. Anal. Appl.}，\textbf{456}（2017），992-1004。在目前的工作中，我们制定的概念，近时代的依赖Riesz空间过程，并表明，如果一个过程是近时代的依赖，无论是强或均匀混合，然后该过程是一个mixingale，提供访问的大数定律。上面的定理适用于Riesz空间中的1阶自回归过程。
英文摘要：
The abstraction of the study of stochastic processes to Banach lattices and vector lattices has received much attention by Grobler, Kuo, Labuschagne, Stoica, Troitsky and Watson over the past fifteen years. By contrast mixing processes have received very little attention. In particular mixingales were generalized to the Riesz space setting in {\sc W.-C. Kuo, J.J. Vardy, B.A. Watson,} Mixingales on Riesz spaces, {\em J. Math. Anal. Appl.}, \textbf{402} (2013), 731-738. The concepts of strong and uniform mixing as well as related mixing inequalities were extended to this setting in {\sc W.-C. Kuo, M.J. Rogans, B.A. Watson,} Mixing inequalities in Riesz spaces, {\em J. Math. Anal. Appl.}, \textbf{456} (2017), 992-1004. In the present work we formulate the concept of near-epoch dependence for Riesz space processes and show that if a process is near-epoch dependent and either strong or uniform mixing then the process is a mixingale, giving access to a law of large numbers. The above is applied to autoregessive processes of order 1 in Riesz spaces.
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