Precise Rates in Log Laws for NA Sequences
Let X1,X2,… be a strictly stationary sequence of negatively associated (NA) random variables with EX1=0, set Sn=X1+⋯+Xn, suppose that σ2=EX12+2∑n=2∞EX1Xn>0 and EX12<∞, if −1<α≤1; EX12(log|X1|)α<∞, if α>1. We prove limε↓0ε2α+2∑n=1∞((logn)α/n)P(|Sn|≥σ(ε+κn)2nlogn)=2−(α+1)(α+1)−1E|N|2α+...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/89107 |
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| _version_ | 1832561224861089792 |
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| author | Yuexu Zhao |
| author_facet | Yuexu Zhao |
| author_sort | Yuexu Zhao |
| collection | DOAJ |
| description | Let X1,X2,… be a strictly stationary sequence of negatively associated (NA)
random variables with EX1=0, set Sn=X1+⋯+Xn, suppose that σ2=EX12+2∑n=2∞EX1Xn>0 and EX12<∞, if −1<α≤1; EX12(log|X1|)α<∞, if α>1. We prove limε↓0ε2α+2∑n=1∞((logn)α/n)P(|Sn|≥σ(ε+κn)2nlogn)=2−(α+1)(α+1)−1E|N|2α+2, where κn=O(1/logn) and N is the standard normal random variable. |
| format | Article |
| id | doaj-art-76079b37b92440a39e3b1be326b2a73e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-76079b37b92440a39e3b1be326b2a73e2025-02-03T01:25:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/8910789107Precise Rates in Log Laws for NA SequencesYuexu Zhao0Institute of Applied Mathematics and Engineering Computation, Hangzhou Dianzi University, Hangzhou 310018, ChinaLet X1,X2,… be a strictly stationary sequence of negatively associated (NA) random variables with EX1=0, set Sn=X1+⋯+Xn, suppose that σ2=EX12+2∑n=2∞EX1Xn>0 and EX12<∞, if −1<α≤1; EX12(log|X1|)α<∞, if α>1. We prove limε↓0ε2α+2∑n=1∞((logn)α/n)P(|Sn|≥σ(ε+κn)2nlogn)=2−(α+1)(α+1)−1E|N|2α+2, where κn=O(1/logn) and N is the standard normal random variable.http://dx.doi.org/10.1155/2007/89107 |
| spellingShingle | Yuexu Zhao Precise Rates in Log Laws for NA Sequences Discrete Dynamics in Nature and Society |
| title | Precise Rates in Log Laws for NA Sequences |
| title_full | Precise Rates in Log Laws for NA Sequences |
| title_fullStr | Precise Rates in Log Laws for NA Sequences |
| title_full_unstemmed | Precise Rates in Log Laws for NA Sequences |
| title_short | Precise Rates in Log Laws for NA Sequences |
| title_sort | precise rates in log laws for na sequences |
| url | http://dx.doi.org/10.1155/2007/89107 |
| work_keys_str_mv | AT yuexuzhao preciseratesinloglawsfornasequences |