On the Local Limit Theorem for Independent Nonlattice 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.

Central and Local Limit Theories in Markov Dependent Random Variables

A Local Limit Theorem for Sums of Independent Random Vectors

We prove a local limit theorem for sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bounded.

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...

On the Lower Limit of Sums of Independent Random Variables

1. Let X1 , X2 , • • • , Xn . . . be independent random variables and let Sn = X, . In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of S n as n -4 co is considered and its true order of magnitude is found with probability one . A counterpart to that problem is to consider the lower limit of Sn as n --> oo and to make a statement about its or...