A curious coincidence in the behavior of ergodic means and (reversed) martingales has
long been known. The problem of investigating this phenomenon was raised and discussed …

MM Rao Carnegie-Mellon University 1. Introduction. At least from the middle 1940's, it was
believed that martingale and ergodic theories, being essentially theories of integration in …

In a paper dedicated to unifying martingales and ergodic averages, Kachurovskiĭ introduced
certain unifying discrete-time martingale ergodic and ergodic martingale processes, for …

The main result of Part I is Theorem 1. This is a maximal theorem for certain operators on
abstract L spaces, where 1? p< oo and E is a Banach space. This theorem contains as …

1. Introduction. The similarity between martingale convergence theorems and ergodic
theorems has been noticed for a long time. This similarity goes beyond the mere statements …

INTRODUCTION Various invariance and central limit theorems for sums of stationary
ergodic processes have been obtained by showing the process to be homologous (see …

Publisher Summary It was felt for a long time that martingales and ergodic theory, being
essentially theories of integration in infinitely many variables, should be obtainable from a …

Introduction. The subject of convergence of martingales of functions with values in a Banach
space was first treated by Scalora [17] and Chatterji [3] who independently showed that a …

The notion of" stopping times" is a useful one in probability theory; it can be applied to both
classical problems and new ones. This book presents this technique in the context of the …

An introduction to martingales appeared in Section 7.4, where convergence theorems for
submartingales {S n, ℱ n, n≥ 1}(relating to differentiation theory) were discussed. Here …