Geodesic
The multidimensional analog of Yu.\,V.~Linnik's theorem on decompositions of a~composition of Gaussian and Poisson laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 742-745

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If the sum of two independent $n$-dimensional random vectors is distributed according to the law which is a composition of $n$-dimensional Gaussian and $n$-dimensional Poisson laws then each of these vectors is distributed according to the law which is a composition of $n$-dimensional Gaussian and $n$-dimensional Poisson laws. 
@article{TVP_1965_10_4_a11,
     author = {I. V. Ostrovskii},
     title = {The multidimensional analog of {Yu.\,V.~Linnik's} theorem on decompositions of a~composition of {Gaussian} and {Poisson} laws},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {742--745},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a11/}
}
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I. V. Ostrovskii. The multidimensional analog of Yu.\,V.~Linnik's theorem on decompositions of a~composition of Gaussian and Poisson laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 742-745. http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a11/