Abstract
Let
be a sequence of series of random variables that are independent within each series, and let k n → ∞ as n → ∞. We set ourselves the task of finding all the limit distributions for sums of the form
as n → ∞. In the absence of additional restrictions, the solution is obvious. Namely, any distribution function F(x) can serve as a limit of this kind. For, if the random variable X n 1 has the distribution function F(x) for every n, and if X nk ≡ 0 for all n and for k > 1, then the sum (1.1) has the distribution F(x) for all n.
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© 1975 Springer-Verlag Berlin · Heidelberg
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Petrov, V.V. (1975). Theorems on Convergence to Infinitely Divisible Distributions. In: Sums of Independent Random Variables. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65809-9_4
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DOI: https://doi.org/10.1007/978-3-642-65809-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65811-2
Online ISBN: 978-3-642-65809-9
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