SMALL DEVIATIONS OF SERIES OF INDEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SMOOTH WEIGHTS

L. V. ROZOVSKY

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SMALL DEVIATIONS OF SERIES OF INDEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SMOOTH WEIGHTS

机译：具有光滑权重的一系列独立非负随机变量的小偏差

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摘要

We study the logarithmic small deviations of Σ_j≧1 λ_jX_j, where {X_j} are independent identically distributed nonnegative random variables and {λ_j} is a sequence of positive and nonincreasing numbers satisfying certain conditions of regularity.

机译：我们研究了Σ_j≥1λ_jX_j的对数小偏差，其中{X_j}是独立的相同分布的非负随机变量，而{λ_j}是满足正则性条件的正数和非递增数的序列。

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《Theory of probability and its applications》 |2013年第1aep期|共17页
作者
L. V. ROZOVSKY;
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正文语种 eng
中图分类概率论与数理统计;
关键词
small deviations; nonnegative random variables; slowly varying function; Laplace transform;

机译：小偏差;负随机变量;缓变函数;拉普拉斯变换;

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专利

1. SMALL DEVIATIONS OF SERIES OF INDEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SMOOTH WEIGHTS [J] . L. V. ROZOVSKY Theory of probability and its applications . 2013,第1aEP期

机译：具有光滑权重的一系列独立非负随机变量的小偏差
2. PROBABILITIES OF SMALL DEVIATIONS OF THE WEIGHTED SUM OF INDEPENDENT RANDOM VARIABLES WITH COMMON DISTRIBUTION THAT DECREASES AT ZERO NOT FASTER THAN A POWER [J] . L. V. Rozovsky Journal of Mathematical Sciences . 2016,第4期

机译：独立随机变量加权和之和的小偏差的概率几乎没有下降，且分布均匀
3. SMALL DEVIATIONS OF PROBABILITIES FOR WEIGHTED SUM OF INDEPENDENT POSITIVE RANDOM VARIABLES WITH A COMMON DISTRIBUTION THAT DECREASES AT ZERO NOT FASTER THAN A POWER [J] . Rozovsky L. V. Theory of probability and its applications . 2015,第1期

机译：独立正随机变量加权和的概率的小偏差，其分布的零值下降不快于幂
4. On the generation of a smooth Gaussian random variable to 5 standard deviations [C] . Muller, G.S., Pauw, . 1988

机译：关于生成5个标准偏差的光滑高斯随机变量
5. The law of the iterated logarithm for weighted averages of independent random variables [D] . Li, Deli 1994

机译：独立随机变量加权平均值的迭代对数定律
6. Precise large deviations for widely orthant dependent random variables with different distributions [O] . Miaomiao Gao, Kaiyong Wang, Lamei Chen -1

机译：具有广泛分布的正态分布随机变量的精确大偏差
7. Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables [O] . A. R. Pruss 1996

机译：关于由独立相同分布的随机变量的总和的偏差概率形成的序列的备率

SMALL DEVIATIONS OF SERIES OF INDEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SMOOTH WEIGHTS

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