GENERALIZED HYPERBOLIC LAWS AS LIMIT DISTRIBUTIONS FOR RANDOM SUMS

V. YU. KOROLEV

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GENERALIZED HYPERBOLIC LAWS AS LIMIT DISTRIBUTIONS FOR RANDOM SUMS

机译：广义双曲线定律作为随机和的极限分布

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A general theorem is proved stating necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to one-parameter variance-mean mixtures of normal laws. As a corollary, necessary and sufficient conditions for convergence of the distributions of sums of a random number of independent identically distributed random variables to generalized hyperbolic laws are obtained. Convergence rate estimates are presented for a particular case of special continuous time random walks generated by compound doubly stochastic Poisson processes.

机译：证明了一个一般性定理，它指出了将随机数的独立相同分布的随机变量之和的分布收敛到法则的一参数方差-均值混合所必需的和充分的条件。作为推论，获得了使随机数的独立相等分布随机变量之和的分布收敛于广义双曲线定律的必要和充分条件。针对由复合双随机泊松过程产生的特殊连续时间随机游动的特定情况，给出了收敛速率估计。

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《Theory of probability and its applications》 |2013年第1aep期|共13页
作者
V. YU. KOROLEV;
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正文语种 eng
中图分类概率论与数理统计;
关键词
random sum; generalized hyperbolic distribution; generalized inverse Gaussian distribution; mixture of probability distributions; identifiable mixtures; additively closed family; convergence rate estimate;

机译：随机和;广义双曲分布;广义高斯逆分布;概率分布的混合;可识别的混合;加法闭族;收敛速度估计;

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2. GENERALIZED HYPERBOLIC LAWS AS LIMIT DISTRIBUTIONS FOR RANDOM SUMS [J] . V. YU. KOROLEV Theory of probability and its applications . 2013,第1aEP期

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3. Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors [J] . Maria Kobus Journal of Multivariate Analysis: An International Journal . 1995,第2期

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GENERALIZED HYPERBOLIC LAWS AS LIMIT DISTRIBUTIONS FOR RANDOM SUMS

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