Geodesic
Limit theorem for the additive replacement process
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 393-404

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A transient discrete-time Markov chain is considered that describes the evolution of the content of an urn with balls having $n$ different colors. At each step the number of balls of a randomly selected color is increased by the number of balls of another randomly selected color. For the case when colors are chosen independently and uniformly, formulas for the first two moments of the numbers of balls are obtained. Under weaker assumptions on the distribution of colors chosen, it is shown that the vector formed by the fractions of balls of $n$ colors has a nondegenerate limit distribution.
Mots-clés : transient Markov chain
Keywords: urn schemes, limit theorems. 
@article{TVP_2017_62_2_a7,
     author = {A. M. Zubkov and K. A. Kolesnikova},
     title = {Limit theorem for the additive replacement process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {393--404},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a7/}
}
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A. M. Zubkov; K. A. Kolesnikova. Limit theorem for the additive replacement process. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 393-404. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a7/