Stochastic Processes An Introduction,9780340806548

Stochastic Processes An Introduction

by ;
ISBN13: 9780340806548
ISBN10: 0340806540
Format: Paperback
Pub. Date: 2001-09-27
Publisher(s): Hodder Education Publishers
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Summary

In this textbook the authors present an accessible introduction to stochastic processes for students in courses that have substantial mathematics or statistics content. It assumes that students have completed the usual first-year methods courses in calculus, differential equations and linear algebra, as well as an introductory course in probability. The book covers random walks, Markov chains, birth and death processes, queues, reliability, and renewal and branching processes.

Author Biography

P W Jones is Professor of Statistics, Keele University P Smith is Professor of Applied Mathematics, Keele University

Table of Contents

Series preface ix
Preface xi
Some background on probability
1(30)
Introduction
1(1)
Probability
1(4)
Conditional probability and independence
5(3)
Discrete random variables
8(2)
Continuous random variables
10(1)
Mean and variance
11(2)
Some standard discrete probability distributions
13(3)
Some standard continuous probability distributions
16(2)
Generating functions
18(5)
Conditional expectation
23(8)
Problems
26(5)
Some gambling problems
31(20)
Gambler's ruin
31(1)
Probability of ruin
31(5)
Some numerical simulations
36(1)
Expected duration of the game
36(5)
Some variations of gambler's ruin
41(10)
Problems
43(8)
Random walks
51(18)
Introduction
51(1)
Unrestricted random walks
52(2)
The probability distribution after n steps
54(3)
First returns of the symmetric random walk
57(1)
Other random walks
58(11)
Problems
60(9)
Markov chains
69(40)
States and transitions
69(1)
Transition probabilities
70(4)
General two-state Markov chains
74(3)
Powers of the transition matrix for the m-state chain
77(9)
Gambler's ruin as a Markov chain
86(2)
Classification of states
88(8)
Classification of chains
96(13)
Problems
101(8)
Poisson processes
109(16)
Introduction
109(1)
The Poisson process
109(3)
Partition theorem approach
112(1)
Iterative method
113(2)
The generating function
115(2)
Variance for the Poisson process
117(1)
Arrival times
118(2)
Summary of the Poisson process
120(5)
Problems
121(4)
Birth and death processes
125(28)
Introduction
125(1)
The birth process
125(3)
Birth process: generating function equation
128(3)
The death process
131(2)
The combined birth and death process
133(4)
General population processes
137(16)
Problems
141(12)
Queues
153(30)
Introduction
153(1)
The single-server queue
154(2)
The stationary process
156(7)
Queues with multiple servers
163(6)
Queues with fixed service times
169(2)
Classification of queues
171(1)
A general approach to the M(λ)/G/1 queue
172(11)
Problems
176(7)
Reliability and renewal
183(16)
Introduction
183(1)
The reliability function
183(3)
Exponential distribution and reliability
186(1)
Mean time to failure
186(1)
Relaibility of series and parallel systems
187(3)
Renewal processes
190(2)
Expected number of renewals
192(7)
Problems
194(5)
Branching and other random processes
199(28)
Introduction
199(1)
Generational growth
199(3)
Mean and variance
202(3)
Probability of extinction
205(2)
Branching processes and martingales
207(4)
Stopping rules
211(2)
The simple epidemic
213(2)
An iterative solution scheme for the simple epidemic
215(12)
Problems
218(9)
Computer simulations and projects
227(12)
Appendix
239(4)
Abbreviations
239(1)
Notation
239(1)
Power series
240(1)
Integrals
240(1)
Matrix algebra
241(1)
Probability distributions
242(1)
References and further reading 243(2)
Answers and comments on some of the end-of-chapter problems 245(10)
Index 255

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