An improvement of convergence rate in the local limit theorem for integral-valued random variables

Central Limit Theorem for Banach Space Valued Fuzzy Random Variables

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.

Central and Local Limit Theories in Markov Dependent Random Variables

A Local Limit Theorem for Sums of Dependent Random Variables

A version of central limit is established normalized sums dependent random when a theorem is and conditional are sufficiently The proof ideas from by representing density as integral of score function a translation of distributions. 1980 Subject 60F99.

On the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables

In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...