This article is cited in 12 papers

A central limit theorem for a sequence of random variables with slowly growing number of dependences

M. B. Petrovskaya, A. M. Leontovič

Moscow

Abstract: We prove a CLT for a sequence of random variables only some of which are dependent. As a consequence we obtain a CLT for random variables characterising the set of the moments of the cell's division in the $m^{th}$ ($m\to\infty$) generation of a specific branching process. The last problem is connected with biological models of cell populations.

Received: 20.12.1977
Revised: 28.04.1980

 English version: Theory of Probability and its Applications, 1983, 27:4, 815–825

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