Short Communications

Local Limit Theorems for Non-Identical Lattice Distributions

V. V. Petrov

Leningrad

Abstract: Asymptotic expansions are obtained in a local limit theorem for the sum of non-identically distributed independent random variables having lattice distributions with finite moments of integer order $k\geq3$. The theorem stated is a generalization of a result by Esseen.

Received: 03.05.1961

 English version: Theory of Probability and its Applications, 1962, 7:3, 333–335