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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 2, Pages 393–404
DOI: https://doi.org/10.4213/tvp5115 (Mi tvp5115) 		 
Short Communications

Limit theorem for the additive replacement process

A. M. Zubkov, K. A. Kolesnikova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tvp5115
Abstract: 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.
Keywords: transient Markov chain, urn schemes, limit theorems.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This research was supported by a grant of the Russian Science Foundation (project 14-50-00005).
Received: 06.02.2017
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 2, Pages 319–327
DOI: https://doi.org/10.1137/S0040585X97T988629
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Zubkov, K. A. Kolesnikova, “Limit theorem for the additive replacement process”, Teor. Veroyatnost. i Primenen., 62:2 (2017), 393–404; Theory Probab. Appl., 62:2 (2018), 319–327
Citation in format AMSBIB
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