The paper deals with the central limit problem for arrays of partially exchangeable random variables. It is shown that, under suitable negligibility conditions, the class of limiting laws coincides with that of exchangeable laws which are presentable as mixtures of infinitely divisible distributions. Moreover necessary and sufficient conditions for convergence to any specified element are provided. An analogous representation is given for mixtures of stable laws.
A central limit problem for partially exchangeable random variables. 1996.
FORTINI, SANDRA;
1996
Abstract
The paper deals with the central limit problem for arrays of partially exchangeable random variables. It is shown that, under suitable negligibility conditions, the class of limiting laws coincides with that of exchangeable laws which are presentable as mixtures of infinitely divisible distributions. Moreover necessary and sufficient conditions for convergence to any specified element are provided. An analogous representation is given for mixtures of stable laws.
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