LOCAL LIMIT THEOREM FOR TRIANGULAR ARRAY OF RANDOM VARIABLES

IGOR A. KORCHINSKY AND ALEXEY M. KULIK

Theory of Stochastic Processes Vol. 13 (29), no. 3, 2007, pp. 48–54

For a triangular array of random variables $\{X_{k,n},k=1,\ldots, c_n; n\in \mathbb{N}\}$ such that for every $n$,the variables $X_{1,n},\ldots,X_{c_n,n}$ are independent and identically distributed, the local limit theorem for the variables $S_n=X_{1,n}+\cdots+X_{c_n,n}$ is established.
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