- 214 pages
- English
- PDF
- Only available on web
Stochastic Convergence
About This Book
Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students.
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Table of contents
- Front Cover
- Stochastic Convergence
- Copyright Page
- Table of Contents
- Preface to the Second Edition
- Preface to the First Edition
- List of Examples
- Chapter 1. INTRODUCTION
- Chapter 2. STOCHASTIC CONVERGENCE CONCEPTS AND THEIR PROPERTIES
- Chapter 3. SPACES OF RANDOM VARIABLES
- Chapter 4. INFINITE SERIES OF RANDOM VARIABLES AND RELATED TOPICS
- Chapter 5. RANDOM POWER SERIES
- Chapter 6. STOCHASTIC INTEGRALS AND DERIVATIVES
- Chapter 7. CHARACTERIZATION OF THE NORMAL DISTRIBUTION BY PROPERTIES OF INFINITE SUMS OF RANDOM VARIABLES
- Chapter 8. CHARACTERIZATION OF SOME STOCHASTIC PROCESSES
- References
- Index