p*-混合随机变量序列加权和的完全收敛性
Complete Convergence of Weighted Sums for ρ *-Mixing Random Variable Sequence
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摘要: 对同分布ρ*-混合随机变量序列{Xn,n≥1},在加权系数{αni,1≤i≤n}满足条件n∑i=1|αni|p=O(nδ),n→∞(0＜δ＜1)和#Ank=#{1≤i≤n:|αni|p＞(k+1)-1}≥ne-1/k下,用截尾法证明了加权和完全收敛性及Marcinkiewicz-Zygmund型强大数定律.
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关键词:
- 完全收敛性,加权和,强大数律
Abstract: For identically distributed ρ* - mixing random variable sequence {Xn, n ≥ 1 }, under the condition that the weighted coefficient {αni, 1 ≤ i≤ n} satisfies n∑i=1|αni||p = O(nδ), n→∞, for some0 ＜δ＜ 1, and # Ank = #{1 ≤ i ≤ n: | αni |p ＞ (k + 1)-1 } ≥ ne-1/k, using truncation methods we prove the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for the weighted sums. -
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