用遍历过程逼近和可测试性

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2024-01-23 DOI:10.1017/jpr.2023.89

Isaac Loh

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引用次数: 0

摘要

我们证明，在所有有限时间间隔内，静态时间序列都可以通过混合过程、非遍历过程、非均值遍历过程和周期过程以及非周期性过程的编码得到均匀近似。一个推论是，在非参数情况下，遍历假说--时间平均值将收敛到其统计对应值--以及几个相邻的假说是不可检验的。此外，还探讨了 Baire 类别的进一步含义。

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Approximation with ergodic processes and testability

We show that stationary time series can be uniformly approximated over all finite time intervals by mixing, non-ergodic, non-mean-ergodic, and periodic processes, and by codings of aperiodic processes. A corollary is that the ergodic hypothesis—that time averages will converge to their statistical counterparts—and several adjacent hypotheses are not testable in the non-parametric case. Further Baire category implications are also explored.

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.