On a certain class of infinitely divisible distributions |
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| Authors: | D. Mejzler |
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| Affiliation: | 1. Institute of Mathematics and Department of Statistics, The Hebrew University of Jerusalem, Jerusalem, Israel
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| Abstract: | We characterize the class of distribution functions Φ(x), which are limits in the following sense: there exist a sequence of independent and equally distributed random variables {ξ n }, numerical sequences {a k }, {b k } and natural numbers {n k } such that $$mathop {lim}limits_{k to infty } Probleft{ {frac{1}{{a_k }}mathop {Sigma }limits_{k = 1}^{n_k } xi _k - b_k< x} right} = Phi (x)$$ and $$mathop {lim inf }limits_{k to infty } (n_k /n_{k + 1} ) > 0$$ . |
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