Almost Sure Asymptotics for Extremes of Non-stationary Gaussian Random Fields 被引量：1

Almost Sure Asymptotics for Extremes of Non-stationary Gaussian Random Fields

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摘要 In this paper, the authors prove an almost sure limit theorem for the maxima of non-stationary Caussian random fields under some mild conditions related to the covariance functions of the Gaussian fields. As the by-products, the authors also obtain several weak convergence results which extended the existing results.

作者 Zhongquan TAN Yuebao Yuebao WANG

机构地区 ol of Mathematical Sciences College of Mathics Isponding author. School of Mathematical Sciences

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2014年第1期125-138,共14页 数学年刊（B辑英文版）

基金 Project supported by the National Natural Science Foundation of China(No.11071182)

关键词 Almost sure limit theorcm EXTREMES Gaussian random fields Non-stationary 随机域非平稳高斯场几乎处处中心极限定理极值协方差函数温和条件极大值

分类号 O211.6 [理学—概率论与数理统计]

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参考文献1

1Guangming ZHUANG,Zuoxiang PENG,Zhongquan TAN.Almost Sure Central Limit Theorem for Partial Sums of Markov Chain[J].Chinese Annals of Mathematics,Series B,2012,33(1):73-82. 被引量：2

二级参考文献16

1Berkes, I., On the almost sure central limit theorem and domains of attraction, Probab. Theory Related Fields, 102, 1995, 1-18.
2Berkes, I. and Csaki, E., A universal result in almost sure central limit theory, Stochastic Process. Appl., 94, 2001, 105-134.
3Brosamler, G., An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc., 104, 1988, 561-574.
4Doukhan, P. and Louhichi, S., A new weak dependenence condition and applications to moment inequali- ties, Stochastic Process. Appl., 84, 1999, 313-342.
5Fahrner, I. and Stadtmuller, U., On almost sure max-limit theorems, Statist. Probab. Left., 37, 1998, 229-236.
6Ibragimov, I. A. and Lifshits, M. A., On the convergence of generalized moments in almost sure central limit theorem, Statist. Probab. Lett., 40, 1998, 343-351.
7Lacey, M. and Philipp, W., A note on the almost everywhere central limit theorem, Statist. Probab. Lett., 9, 1990, 201-205.
8Leadbetter, M. R., Lindgren, G. and Rootzen, H., Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, Berlin, 1983.
9Matula, P., On the almost sure central limit theorem for associated random variables, Probab. Math. Statist., 18, 1998, 411-416.
10Peligrad, M. and Shao, Q., A note on the almost sure central limit theorem for weakly dependent random variables, Statist. Probab. Lett., 22, 1995, 131-136.