A martingale central limit theorem without negligibility conditions

A Martingale Central Limit Theorem

We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.

The Martingale Central Limit Theorem

One of the most useful generalizations of the central limit theorem is the martingale central limit theorem of Paul Lévy. Lévy was in part inspired by Lindeberg’s treatment of the central limit theorem for sums of independent – but not necessarily identically distributed – random variables. Lindeberg formulated what, in retrospect, is the right hypothesis, now known as the Lindeberg condition,1...

Martingales, Lévy’s continuity theorem, and the martingale central limit theorem

A Purely Martingale Version of Lindeberg's Central Limit Theorem

Martingale Central Limit Theorem and Nonuniformly Hyperbolic Systems

MARTINGALE CENTRAL LIMIT THEOREM FOR NONUNIFORMLY HYPERBOLIC SYSTEMS SEPTEMBER 2013 LUKE MOHR, B.S., UNIVERSITY AT BUFFALO M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor HONG-KUN ZHANG In this thesis we study the central limit theorem (CLT) for nonuniformly hyperbolic dynamical systems. We examine cases in which polynomial decay of co...