Stochastic Processes: An Introduction

2nd Edition

P W Jones and P Smith

CRC Press (http://crcpress.com/product/isbn/9781420099607)

ISBN 978-1-4200-9960-7
©2009 P W Jones and P Smith

 Front Cover

Contents | Solutions Manual | Mathematica Programs | Programs in R

Contents

1    Some Background in 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
    Problems
 
2    Some Gambling Problems
  2.1 Gambler's ruin
  2.2 Probability of ruin
  2.3 Some numerical simulations
  2.4 Expected duration of the game
  2.5 Some variations of gambler's ruin
    Problems
 
3    Random Walks
  3.1 Introduction
  3.2 Unrestricted random walks
  3.3 Probability distribution after n steps
  3.4 First returns of the symmetric random walk
  3.5 Other random walks
    Problems
 
4    Markov Chains
  4.1 States and transitions
  4.2 Transition probabilities
  4.3 General two-state Markov chain
  4.4 Powers of the transition matrix for the m-state chain
  4.5 Gambler's ruin as a Markov chain
  4.6 Classification of states
  4.7 Classification of chains
    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 Variance for the Poisson process
  5.7 Arrival times
  5.8 Summary of the Poisson process
    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
    Problems
 
7    Queues
  7.1 Introduction
  7.2 The single server queue
  7.3 The stationary process
  7.4 Queues with multiple servers
  7.5 Queues with fixed service times
  7.6 Classification of queues
  7.7 A general approach to the M(λ)/G/1 queue
    Problems
 
8    Reliability and Renewal
  8.1 Introduction
  8.2 The reliability function
  8.3 The 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
    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 The simple epidemic
  9.8 An iterative scheme for the simple epidemic
    Problems
 
10    Computer Simulations and Projects
 
    Appendix
 
    References and Further Reading
 
    Answers and Comments on some of the end-of-chapter Problems