A note on the strong law of large numbers for associated sequences
We prove that the sequence {bn−1∑i=1n(Xi−EXi)}n≥1 converges a.e. to zero if {Xn,n≥1} is anassociated sequence of random variables with ∑n=1∞bkn−2Var(∑i=kn−1+1knXi)<∞ where {bn,n≥1} is a positive nondecreasing sequence and {kn,n≥1} is a strictly increasing sequence, both tending to infinity as n t...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3195 |
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| Summary: | We prove that the sequence {bn−1∑i=1n(Xi−EXi)}n≥1 converges a.e. to zero if {Xn,n≥1} is anassociated sequence of random variables with ∑n=1∞bkn−2Var(∑i=kn−1+1knXi)<∞ where {bn,n≥1} is a positive nondecreasing sequence and {kn,n≥1} is a strictly increasing sequence, both tending to infinity as n tends to infinity and 0<a=infn≥1bknbkn+1−1≤supn≥1bknbkn+1−1=c<1. |
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| ISSN: | 0161-1712 1687-0425 |