Short Communications

On the necessity of the Lyapunov condition for normal convergence

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: This paper provides necessary and sufficient conditions for the weak convergence of the distributions of sums of independent random variables to the normal distribution. The conditions are given as a combination of a part of the assumption of the classic criterion for the normal convergence and the Lyapunov condition for truncated random variables.

Keywords: normal convergence, Lindeberg–Feller theorem, weak convergence, Lyapunov condition.

Received: 04.05.2005

DOI: 10.4213/tvp11

 English version: Theory of Probability and its Applications, 2008, 52:1, 164–166

Bibliographic databases:

• 
• 
• 
• 
•