關於φ-mixing隨機變數完全動量收歛之研究

A study on complete moment convergence for φ-mixing random variables

黃照棡(Chao-Kang Huang)

指導教授 ： 胡殿中

國立清華大學/理學院/數學系/碩士(2007年)

摘要

在這篇論文裡,我們首先複習一些前人在φ-mixing或NA和獨立的假設下關於移動平均完全收斂和完全動量收斂的結果。然後我們證明了在 是φ-mixing隨機變數一致分佈數列下移動平均過程最大部分和的完全動量收斂性。

關鍵字

完全動量收斂 ； φ-mixing隨機變數

並列摘要

In this thesis, we first review some previous results about
complete convergence and complete moment convergence of moving average processes under dependence ($varphi-mixing$ or negatively associated) and independence assumption. And then we show that the complete moment convergence of the maximal partial sums of moving average processes ${sum_{i=-infty}^{infty}a_iY_{i+n},ngeq 1}$ under the assumption that ${Y_{i},-infty

並列關鍵字

complete moment convergence ； φ-mixing random variables

參考文獻

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[4] Chen, P., Hu, T.C. and Volodin, A. (2007), Limiting behavior of moving average process under φ-mixing assumption, preprint.

[5] Chen, P., Hu, T.C. and Volodin, A. (2007), Complete convergence and complete moment convergence of moving average process of negatively associated random variables, preprint.

[6] Chow, Y.S. (1988), On the rate of moment convergence of sample sums and extremes, Bulletin of the Institute of Mathematics Academia Sinica, 16, 3, 177-201.