Asymptotic normality in a scheme of finitely dependent distribution of particles in cells

A scheme of finitely dependent (and, generally speaking, nonstationary) distribution of particles in a countable collection of cells is considered. Sufficient conditions are given for asymptotic normality of the random variables $\mu_r$ (the number of cells containing exactly $r$ particles each), $\mu$ (the number of occupied cells), and $\xi_r$ (the number of $r$-fold repetitions). For $\mu_r$ these conditions correspond to the “left intermediate domain of variation of the parameters”, while for $\xi_r$ they include also the “central domain”. The method of moments is used in the proof.
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