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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 2, Pages 393–404 (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

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


DOI: https://doi.org/10.4213/tvp5115

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English version:
Theory of Probability and its Applications, 2018, 62:2, 319–327

Bibliographic databases:

Document Type: Article
Received: 06.02.2017

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

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