Functional Erdős-Renyi laws for semiexponential random variables
Functional Erdős-Renyi laws for semiexponential random variables
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半指数随机变量的函数 Erdős-Renyi 定律
DOI：
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发表时间：
1998
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通讯作者：
N. Gantert
中科院分区：
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作者：
N. Gantert
做个身份证。半指数分布的随机变量序列，给出了部分和的Erdos-Renyi律的函数形式。与经典的情形相反，即随机变量具有所有阶的指数矩的情形，极限点的集合不是连续函数的子集。这反映了极端值的更大影响。证明是基于相应的随机游走的轨迹的大偏差原则。这种大偏差原则中的标准化不同于通常的标准化，并且取决于分布的尾部。以同样的方式，我们证明了移动平均线的函数极限定律。
For an i.i.d. sequence of random variables with a semiexponential distribution, we give a functional form of the Erdos-Renyi law for partial sums. In contrast to the classical case, that is, the case where the random variables have exponential moments of all orders, the set of limit points is not a subset of the continuous functions. This reflects the bigger influence of extreme values. The proof is based on a large deviation principle for the trajectories of the corresponding random walk. The normalization in this large deviation principle differs from the usual normalization and depends on the tail of the distribution. In the same way, we prove a functional limit law for moving averages.