Topics in Stochastic Processes

Probability and Mathematical Statistics: A Series of Monographs and Textbooks

Robert B. Ash, Melvin F. Gardner, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780120652709
• eBook ISBN:
  9781483191430
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.

Table of contents

• Front Cover
• Topics in Stochastic Processes
• Copyright Page
• Table of Contents
• PREFACE
• Chapter 1. L2 Stochastic Processes
• Chapter 2. Spectral Theory and Prediction
• Chapter 3. Ergodic Theory
• Chapter 4. Sample Function Analysis of Continuous Parameter Stochastic Processes
• Chapter 5. The Itô Integral and Stochastic Differential Equations
• Appendix 1: Some Results from Complex Analysis
• Appendix 2: Fourier Transforms on the Real Line
• References
• Solutions to Problems
• Index