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 ofpartial sums of independent random variables.Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Ornstein-Uhlenbeck processes. Audience:Researchers whose work involves probability theory and statistics.
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目录
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 Resuits 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 CsÖrgÓ-Révész Increments? 2.4 On the Increments Without Moment Hypotheses 2.5 How Small Are the Increments of Partial Sums of Independent R.V.'s? 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 l的2次方-Norm Squared Process 3.5 Two-Parameter Gaussian Process with Kernel References