Geodesic
On the decomposition of lattice distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 589-596

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This work provides some results on the convolutions of a special kind of signed measure known as the Poisson signed measure. We show a simple way of obtaining asymptotic decompositions into convolutions of Poisson signed measure that is appropriate for a broad range of lattice distributions. The work demonstrates the analogy between such decompositions and the classic Gram–Charlier decompositions of type $A$ and $B$, and the Edgeworth-Cramer series.
Keywords: Poisson signed measure, convolutions of Poisson signed measure, asymptotic decompositions, lattice random variables. 
@article{TVP_2004_49_3_a8,
     author = {D. N. Karymov},
     title = {On the decomposition of lattice distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {589--596},
     publisher = {mathdoc},
     volume = {49},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a8/}
}
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D. N. Karymov. On the decomposition of lattice distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 589-596. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a8/