Geodesic
Estimations of the stability of decompositions for the compositions of the Gauss and Poisson distributions
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 3, Tome 87 (1979), pp. 164-186 Cet article a éte moissonné depuis la source Math-Net.Ru

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The uniform metric estimates accurate to the order of magnitude are obtained for this stability. Besides two-sided estimates (close to each other in a certain sense) are obtained for the stability in the Levy metric. 
@article{ZNSL_1979_87_a13,
     author = {G. P. Chistyakov},
     title = {Estimations of the stability of decompositions for the compositions of the {Gauss} and {Poisson} distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--186},
     year = {1979},
     volume = {87},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_87_a13/}
}
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G. P. Chistyakov. Estimations of the stability of decompositions for the compositions of the Gauss and Poisson distributions. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 3, Tome 87 (1979), pp. 164-186. http://geodesic.mathdoc.fr/item/ZNSL_1979_87_a13/