Stochastic Processes and Their Applications,9780415272322

Stochastic Processes and Their Applications

by ;
ISBN13: 9780415272322
ISBN10: 0415272327
Format: Hardcover
Pub. Date: 2001-10-18
Publisher(s): CRC Press
List Price: $120.00

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Summary

Presents stochastic processes in a comprehensive, user-friendly and accessible way containing numerous worked examples. Authors include important proofs and theoretically challenging examples and exercises, thus making the book attractive to those whose interest is more mathematical.

Author Biography

Frank E. Beichelt is a professor of operations research in the Department of Statistics and Actuarial Science at the University of Witwatersrand, Johannesburg, Republic of South Africa. Previously he was a professor of mathematics and head of the Department of Mathematics at the University of Engineering, Mittweida, Germany. He has published widely in the field of maintenance and reliability theory. L. Paul Fatti is a professor of statistics and head of the Department of Statistics and Actuarial Science at the University of Witwatersrand, Johannesburg, Republic of South Africa. He has been president of both the South African Statistical Association and the Operations Research Society of South Africa, and he consults for a wide range of organisations in both statistics and operations research.

Table of Contents

Preface ix
Symbols and Abbreviations xi
Probability Theory
1(42)
Random Events and Their Probabilities
1(3)
Random Variables
4(9)
Discrete Random Variables
4(2)
Continuous Random Variables
6(2)
Nonnegative Random Variables
8(5)
Random Vectors
13(9)
Two-Dimensional Random Vectors
13(7)
n-Dimensional Random Vectors
20(2)
Sums and Sequences of Random Variables
22(9)
Transformations of Probability Distributions
31(12)
z-Transformation
32(2)
Laplace-Transformation
34(3)
Exercises
37(6)
Stochastic Processes
43(26)
Introduction
43(4)
Characteristics of Stochastic Processes
47(2)
Properties of Stochastic Processes
49(4)
Special Stochastic Processes
53(16)
Continuous-Time Stochastic Processes
53(7)
Stationary Discrete-Time Stochastic Processes
60(7)
Exercises
67(2)
Poisson Processes
69(30)
Homogeneous Poisson Processes
69(16)
Definition and Properties
69(8)
Poisson Process and Uniform Distribution
77(8)
Inhomogeneous Poisson Process
85(14)
Definition and Properties
85(4)
Minimal Repair
89(8)
Exercises
97(2)
Renewal Processes
99(38)
Foundations
99(3)
Renewal Function
102(9)
Renewal Equations
102(5)
Bounds for the Renewal Function
107(4)
Recurrence Times
111(3)
Asymptotic Behaviour
114(4)
Stationary Renewal Processes
118(2)
Alternating Renewal Processes
120(5)
Cumulative Stochastic Processes
125(6)
Regenerative Stochastic Processes
131(6)
Exercises
134(3)
Discrete-Time Markov Chains
137(32)
Foundations and Examples
137(8)
Classification of States
145(13)
Closed Sets of States
145(2)
Equivalence Classes
147(3)
Periodicity
150(2)
Recurrence and Transience
152(6)
Limit Theorems and Stationary Distribution
158(5)
Birth-and Death Processes
163(6)
Exercises
165(4)
Continuous-Time Markov Chains
169(88)
Foundations
169(4)
Kolmogorov's Differential Equations
173(10)
Stationary State Probabilities
183(4)
Construction of Markovian Systems
187(2)
Erlang's Phase Method
189(2)
Birth- and Death Processes
191(16)
Time-Dependent State Probabilities
191(11)
Stationary State Probabilities
202(5)
Sojourn Times
207(2)
Applications in Queueing Theory
209(32)
Introduction
209(3)
Loss Systems
212(4)
Waiting Systems
216(3)
Waiting-Loss-Systems
219(4)
Special Single-Server Queueing Systems
223(6)
Networks of Queueing Systems
229(12)
Semi-Markov Processes
241(16)
Exercises
250(7)
Wiener Processes
257(36)
Definition and Properties
257(6)
First Passage Times
263(6)
Transformations of the Wiener Process
269(24)
Elementar Transformations
269(2)
Ornstein-Uhlenbeck Process
271(1)
Wiener-Process with Drift
272(13)
Integral Transformations
285(4)
Exercises
289(4)
Spectral Analysis of Stationary Processes
293(19)
Foundations
293(2)
Processes with Discrete Spectrum
295(4)
Processes with Continuous Spectrum
299(13)
Spectral Representation of the Covariance Function
299(9)
Spectral Representation of Stationary Processes
308(2)
Exercises
310(2)
Appendix 1 Landau Order Symbol 312(1)
Appendix 2 Dirac Delta Function 313(1)
Answers to Selected Exercises 314(5)
References 319(4)
Index 323

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