This Volume presents an up-to-date overview of the most significant developments concerning strong approximation and strong convergence in probability theory.The book comprises three chapters. The first deals with wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Omstein-Uhlenbeck processes.

 This Volume presents an up-to-date overview of the most significant developments concerning strong approximation and strong convergence in probability theory.The book comprises three chapters. The first deals with wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Omstein-Uhlenbeck processes.

 Audience:Researchers whose work involves probability theory and statistics.

Series Editor's Preface                  

Preface                        

1. The Increments of a Wiener and Related Gaussian Processes

1.1 How Large Are the Increments of a Wiener Process?

1.2 Some Inferior Limit Results for the Increments of a Wiener Process

1.3 Further Discussion for Increments of a Wiener Process

1.4 How Large Are the Increments of a Two-Parameter Wiener Process?

1.5 The Increments of a Non-Stationary Gaussian Process

2. The Increments of Partial Sums of Independent Random Variables

2.1 Introduction

2.2 How Large Are the Lag Sums?

2.3 How Large Are the Csorgo-Revesz Increments?

2.4 On the Increments Without Moment Hypotheses

2.5 How Small Are the Increments of Partial Sums of Independent

2.6 A Study of Partial Sums with the Help of Strong Approximation

3. Strong Laws of the Processes Generated by Infinite Dimensional Ornstein-Uhlenbeck Processes

3.1 Introduction

3.2 Partial Sum Process

3.3 Infinite Series

3.4 F-Norm Squared Process

3.5 Two-Parameter Gaussian Process with Kernel

References