The Edgeworth Expansion and Convergence in the Central Limit Theorem

Edgeworth Expansion on N{spheres and Jacobi Hypergroups

Suitable normalization of time{homogeneous rotation{invariant random walks on unit spheres S d R d+1 for d > 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted to an associated Edgeworth expansion with respect to the total variation norm. This strong type of convergence is diierent from the classical case. The proof is performed in the more general setting o...

Rate of Convergence and Edgeworth-type Expansion in the Entropic Central Limit Theorem1 by Sergey

Fisher information and the central limit theorem

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

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...

Central and Local Limit Theories in Markov Dependent Random Variables