Martingale limit theory

Abstract

A central limit theorem for martingales was considered as early as 1935» when Paul Levy established several results. However, it is only since the 1960's that the field has received much attention, and some of the most important work was published by Erown [9] in 1971. In this dissertation we take a critical look at the present situation of martingale central limit theory. We change the form of the classical central limit problem and show that in this new form it has a solution under more general conditions. This leads us to analogous results for reverse martingales, and to a new form of the law of the iterated logarithm. Show more