Local limit theorems for sums of independent random vectors (Q1117563)
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scientific article; zbMATH DE number 4092463
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local limit theorems for sums of independent random vectors |
scientific article; zbMATH DE number 4092463 |
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Local limit theorems for sums of independent random vectors (English)
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1987
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[For the entire collection see Zbl 0626.00025.] Let \(p_ n(x)\) and \(q_ n(x)\) be the densities of the n-fold convolutions of the distributions F and G, respectively. We prove estimates for \(\sup_{x}| p_ n(x)-q_ n(x)|\), expressed in terms of moment characteristics of F-G, under certain restrictions on the densities of F and G. Similar problems are solved for two lattice distributions and for a lattice and a continuous distribution.
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local limit theorems
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convolutions
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lattice distributions
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