强混合序列部分和乘积的渐近正态性

J4 ›› 2009, Vol. 47 ›› Issue (6): 1196-1198.

Previous Articles Next Articles

Asymptotic Distribution of the Product of Strong Mixing Sums

LIU Jun¹, WANG Xingang², ZHANG Dongmei³

1. College of Mathematics, Beihua University, Jilin 132013, Jilin Province, China;2. College of Information Engineering, Zhejiang University of Technology, Hangzhou 310032, China;3. College of Science, Zhejiang University of Technology, Hangzhou 310032, China

Received:2009-03-10 Online:2009-11-26 Published:2010-01-07
Contact: LIU Jun E-mail:liujun6078@126.com.

Abstract

Abstract:

Let {X_n,n≥1} be a sequence of strong mixing identically distributed positive random variable, under some suitable conditions, by means of the central limit theorem and the law of large numbers of strong mixing sequence, it is proved that and N is a standrad normal random variable.

Key words: strong mixing sequences, product of sums, central limit theorem, identically distribution, lognormal distribution

CLC Number:

O211.4

LIU Jun, WANG Xingang, ZHANG Dongmei. Asymptotic Distribution of the Product of Strong Mixing Sums[J].J4, 2009, 47(6): 1196-1198.

[1]	ZHAO Jiayu, LU Dongmei. Asymptotic Distribution of Products of Partial Sums under NSD Sequences [J]. Journal of Jilin University Science Edition, 2020, 58(6): 1339-1344.
[2]	LI Jingyu, ZHANG Yong. Central Limit Theorem for Linear ProcessesGenerated by NSD Sequences#br# [J]. Journal of Jilin University Science Edition, 2019, 57(2): 300-304.
[3]	HE Bing, BO Xiaoling. Test of Equality of TwoSample HighDimensional Covariance Matrices Based on Random F-Matrix#br# [J]. Journal of Jilin University Science Edition, 2019, 57(1): 65-71.
[4]	PANG Yuxin, WANG Dehui, TAN Xili. Random Index Central Limit Theorem for LPQD Sequence [J]. Journal of Jilin University Science Edition, 2018, 56(5): 1119-1124.
[5]	GUAN Lihong, LI Yinghong. A Note on Almost Sure Central Limit Theorems for Random Sequences [J]. Journal of Jilin University Science Edition, 2018, 56(2): 306-310.
[6]	ZHAO Jiayu, GAO Ruimei. Note on the Almost Sure Central Limit Theorem forProduct of Trimmed Sums [J]. Journal of Jilin University Science Edition, 2016, 54(05): 1036-1038.
[7]	LI Yuan, XU Feng. Note on Almost Sure Central Limit Theorem forProduct of Partial Sums of ρ^--Mixing Sequences [J]. Journal of Jilin University Science Edition, 2016, 54(04): 785-789.
[8]	CAO Yang, WU Qunying. Almost Sure Central Limit Theorem for Products ofSums of Partial Sums for ρ^--Mixing Sequences [J]. Journal of Jilin University Science Edition, 2015, 53(06): 1151-1155.
[9]	LIU Yanping, WU Qunying, YANG Fei. Almost Sure Limit Theorem for Maximum Gaussian Random Fields [J]. Journal of Jilin University Science Edition, 2015, 53(06): 1145-1150.
[10]	JU An-Yu, ZHANG Yong. Almost Sure Central Limit Theorem for Products ofSums of Partial Sums for ρ^-Mixing Sequences [J]. J4, 2012, 50(06): 1129-1134.
[11]	FENG Feng-Xiang. Almost Sure Central Limit Theorem for the Productof Partial Sums of i.i.d Positive Variables [J]. J4, 2012, 50(02): 270-274.
[12]	YANG Jin-Yang. Asymptotic Distribution of Products of Sumsof Partial Sums under ρ-Mixng Sequence [J]. J4, 2012, 50(02): 258-262.
[13]	ZHANG Yong. A Note on \|Almost Sure Central Limit Theorem forUniform Empirical Processes [J]. J4, 2011, 49(04): 687-689.
[14]	XIE Da-Xiang, TUN Qun-Yang. Popularization of Almost Sure Central Limit Theoremof Sequence of Random Element [J]. J4, 2011, 49(02): 251-254.
[15]	LIU Jun. lmost Sure Central Limit Theorem for Weighted Sumsunder α-Weak Dependence [J]. J4, 2011, 49(01): 79-81.

Asymptotic Distribution of the Product of Strong Mixing Sums

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10