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