A Local Limit Theorem for Sums of Independent Random Vectors

The Almost Sure Local Central Limit Theorem for the Product of Partial Sums

We derive under some regular conditions an almost sure local central limit theorem for the product of partial sums of a sequence of independent identically distributed positive random variables.

Central and Local Limit Theories in Markov Dependent Random Variables

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...

Multivariate normal approximations by Stein’s method and size bias couplings

Stein’s method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias coupling, which we discuss in studying the approximation of distributions of sums of dependent random vectors. In the univariate case, we briefly illustrate ...

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.