An elementary proof of the local central limit theorem
The authors give a proof (characteristic functions free) of the local central limit theorem for independent non-identically distributed integer valued random variables. The first theorem is formulated for the sum of \(n\) random variables. This theorem is restated for the triangular arrays of variables. The theorems have some interesting consequences. The vector-variable analog of the second theorem is also proved for an array of independent \(L\)-valued random vectors. \(L\) denotes the \(d\)-dimensional integer lattice.
scientific article; zbMATH DE number 806436