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Stochastic Processes An Introduction 3rd edition by Peter Watts Jones, Peter Smith ISBN 0367657600‎ 978-0367657604

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ISBN 10: 0367657600
ISBN 13:‎ 978-0367657604
Author: Peter Watts Jones, Peter Smith

Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues.

The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference.

This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.

Stochastic Processes An Introduction 3rd Table of contents:

1. Some Background on Probability

1.1 Introduction

1.2 Probability

1.3 Conditional probability and independence

1.4 Discrete random variables

1.5 Continuous random variables

1.6 Mean and variance

1.7 Some standard discrete probability distributions

1.8 Some standard continuous probability distributions

1.9 Generating functions

1.10 Conditional expectation

1.11 Problems

2. Some Gambling Problems

2.1 Gambler’s ruin

2.2 Probability of ruin

2.3 Some numerical simulations

2.4 Duration of the game

2.5 Some variations of gambler’s ruin

2.5.1 The infinitely rich opponent

2.5.2 The generous opponent

2.5.3 Changing the stakes

2.6 Problems

3. Random Walks

3.1 Introduction

3.2 Unrestricted random walks

3.3 The exact probability distribution of a random walk

3.4 First returns of the symmetric random walk

3.5 Problems

4. Markov Chains

4.1 States and transitions

4.2 Transition probabilities

4.3 General two-state Markov chains

4.4 Powers of the general transition matrix

4.5 Gambler’s ruin as a Markov chain

4.6 Classification of states

4.7 Classification of chains

4.8 A wildlife Markov chain model

4.9 Problems

5. Poisson Processes

5.1 Introduction

5.2 The Poisson process

5.3 Partition theorem approach

5.4 Iterative method

5.5 The generating function

5.6 Arrival times

5.7 Summary of the Poisson process

5.8 Problems

6. Birth and Death Processes

6.1 Introduction

6.2 The birth process

6.3 Birth process: Generating function equation

6.4 The death process

6.5 The combined birth and death process

6.6 General population processes

6.7 Problems

7. Queues

7.1 Introduction

7.2 The single-server queue

7.3 The limiting process

7.4 Queues with multiple servers

7.5 Queues with fixed service times

7.6 Classification of queues

7.7 Problems

8. Reliability and Renewal

8.1 Introduction

8.2 The reliability function

8.3 Exponential distribution and reliability

8.4 Mean time to failure

8.5 Reliability of series and parallel systems

8.6 Renewal processes

8.7 Expected number of renewals

8.8 Problems

9. Branching and Other Random Processes

9.1 Introduction

9.2 Generational growth

9.3 Mean and variance

9.4 Probability of extinction

9.5 Branching processes and martingales

9.6 Stopping rules

9.7 A continuous time epidemic

9.8 A discrete time epidemic model

9.9 Deterministic epidemic models

9.10 An iterative solution scheme for the simple epidemic

9.11 Problems

10. Brownian Motion: Wiener Process

10.1 Introduction

10.2 Brownian motion

10.3 Wiener process as a limit of a random walk

10.4 Brownian motion with drift

10.5 Scaling

10.6 First visit times

10.7 Other Brownian motions in one dimension

10.8 Brownian motion in more than one dimension

10.9 Problems

11. Computer Simulations and Projects

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