Geodesic
Asymptotic behaviour of a~multinomial distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 826-831

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Let $P_n(m_1,\dots,m_k)$ be the probability of a multinomial distribution and $\Pi_1$ , $\Pi_2$ and $\Pi_3$ be multidimensional distributions: Poisson, Gaussian and a combination of them respectively. Asymptotic estimates for the sums $$ \sum_{m_1+\dots+m_k=n}|P_n-\Pi_i|\qquad(i=1,2,3) $$ are obtained. 
@article{TVP_1976_21_4_a10,
     author = {N. {\CYRK}. Arenbaev},
     title = {Asymptotic behaviour of a~multinomial distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {826--831},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a10/}
}
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N. К. Arenbaev. Asymptotic behaviour of a~multinomial distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 826-831. http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a10/