On Chung’s Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups
On Chung’s Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups
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关于单连通第 2 步-幂零李群的钟大数定律
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发表时间：
2014
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通讯作者：
D. Neuenschwander
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作者：
D. Neuenschwander
Ordóñez Cabrera和Sung（2002）证明了在一定的“矩”条件下，对于加权banach值随机变量的三角形数组，a.s.收敛、收敛于L1、收敛于概率和完全收敛于0是等价的，从而给出了Chung大数定律的一个变种。我们将他们的结果（在稍微尖锐的技术条件下）推广到单连通2阶幂零李群上的对称随机变量。
Ordóñez Cabrera and Sung (2002) have proved that under certain “moment” conditions, for triangular arrays of weighted Banach-valued random variables, a.s. convergence, convergence in L1, convergence in probability, and complete convergence to 0 are equivalent, thus giving a variant of Chung’s law of large numbers. We extend their result (under slightly sharper technical conditions) to symmetric random variables on simply connected step 2-nilpotent Lie groups.