A First Course in Stochastic Processes

Samuel Karlin, Howard E. Taylor

• Publisher: Academic Press
• Year: 2012
• ISBN:
  9780080570419
• Edition: 2
• Topic: Matematica
• Subtopic: Analisi matematica

The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.

The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.

Table of contents

• Front Cover
• A First Course In Stochastic Processes
• Copyright Page
• Table of Contents
• Preface
• Preface to First Edition
• Chapter 1. ELEMENTS OF STOCHASTIC PROCESSES
• Chapter 2. MARKOV CHAINS
• Chapter 3. THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS
• Chapter 4. CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS
• Chapter 5. RENEWAL PROCESSES
• Chapter 6. MARTINGALES
• Chapter 7. BROWNIAN MOTION
• Chapter 8. BRANCHING PROCESSES
• Chapter 9. STATIONARY PROCESSES
• Appendix: REVIEW OF MATRIX ANALYSIS
• Index