A first course in stochastic processes / Samuel Karlin, Howard M. Taylor.

Includes bibliographical references and index.

Front Cover; A First Course In Stochastic Processes; Copyright Page; Table of Contents ; Preface; Preface to First Edition; Chapter 1. ELEMENTS OF STOCHASTIC PROCESSES; 1. Review of Basic Terminology and Properties of Random Variables and Distribution Functions; 2. Two Simple Examples of Stochastic Processes; 3. Classification of General Stochastic Processes; 4. Defining a Stochastic Process; Elementary Problems; Problems; Notes; References; Chapter 2. MARKOV CHAINS; 1. Definitions; 2. Examples of Markov Chains; 3. Transition Probability Matrices of a Markov Chain. 4. Classification of States of a Markov Chain5. Recurrence; 6. Examples of Recurrent Markov Chains; 7. More on Recurrence; Elementary Problems; Problems; Notes; References; Chapter 3. THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS; 1. Discrete Renewal Equation; 2. Proof of Theorem 1.1; 3. Absorption Probabilities; 4. Criteria for Recurrence; 5. A Queueing Example; 6. Another Queueing Model; 7. Random Walk; Elementary Problems; Problems; Notes; Reference; Chapter 4. CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS; 1. General Pure Birth Processes and Poisson Processes. 2. More about Poisson Processes3. A Counter Model; 4. Birth and Death Processes; 5. Differential Equations of Birth and Death Processes; 6. Examples of Birth and Death Processes; 7. Birth and Death Processes with Absorbing States; 8. Finite State Continuous Time Markov Chains; Elementary Problems; Problems; Notes; References; Chapter 5. RENEWAL PROCESSES; 1. Definition of a Renewal Process and Related Concepts; 2. Some Examples of Renewal Processes; 3. More on Some Special Renewal Processes; 4. Renewal Equations and the Elementary Renewal Theorem; 5. The Renewal Theorem. 6. Applications of the Renewal Theorem7. Generalizations and Variations on Renewal Processes; 8. More Elaborate Applications of Renewal Theory; 9. Superposition of Renewal Processes; Elementary Problems; Problems; Reference; Chapter 6. MARTINGALES; 1. Preliminary Definitions and Examples; 2. Supermartingales and Submartingales; 3. The Optional Sampling Theorem; 4. Some Applications of the Optional Sampling Theorem; 5. Martingale Convergence Theorems; 6. Applications and Extensions of the Martingale Convergence Theorems; 7. Martingales with Respect to v-Fields; 8. Other Martingales. Elementary ProblemsProblems; Notes; References; Chapter 7. BROWNIAN MOTION; 1. Background Material; 2. Joint Probabilities for Brownian Motion; 3. Continuity of Paths and the Maximum Variables; 4. Variations and Extensions; 5. Computing Some Functionals of Brownian Motion by Martingale Methods; 6. Multidimensional Brownian Motion; 7. Brownian Paths; Elementary Problems; Problems; Notes; References; Chapter 8. BRANCHING PROCESSES; 1. Discrete Time Branching Processes; 2. Generating Function Relations for Branching Processes; 3. Extinction Probabilities; 4. Examples

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 processe