Dynamic Probabilistic Systems, Volume I Markov Models

by Howard, Ronald A.

• ISBN13: 9780486458700
• ISBN10: 0486458709
• Format: Paperback
• Copyright: 2007-06-05
• Publisher: Dover Publications

Summary

This book is an integrated work published in two volumes. the first volume treats the basic Markov process and its variants; the second, semi-Markov and decision processes. It equips readers to formulate, analyze, and evaluate simple and advanced Markov models of systems, ranging from genetics to space engineering to marketing. 1971 edition.

Author Biography

Ronald A. Howard, Professor of Management Science and Engineering at Stanford University

Table of Contents

The Basic Markov Process	p. 1
Introduction	p. 1
Markov Process Behavior	p. 6
State Probabilities	p. 12
The Transient Behavior of State Probabilities-Shrinkage	p. 19
Transform Analysis	p. 43
Transform Analysis of Markov Processes	p. 59
Conclusion	p. 81
Systems Analysis of Linear Processes	p. 89
Properties and Models of Simple Systems	p. 89
Complex Systems	p. 99
Transform Analysis of Systems	p. 103
Flow Graph Reduction	p. 114
An Inspection Method for Flow Graph Reduction	p. 124
An Inventory System Example	p. 127
Matrix Systems	p. 136
Complex Matrix Systems	p. 140
Conclusion	p. 152
Systems Analysis of Markov Processes	p. 161
Flow Graph Analysis of Markov Processes	p. 161
Matrix Flow Graph Analysis of Markov Processes	p. 175
Transient Markov Processes	p. 189
Transient Processes	p. 189
Some Applications of Transient Processes-Coin-Tossing	p. 220
Holding-Time Statistics	p. 240
Markov Process Statistics	p. 257
State Occupancy Statistics	p. 257
First Passage Times	p. 286
Transitions: Statistics and Inference	p. 325
Tagging	p. 325
Processes with Partial Information	p. 349
Inference	p. 361
Recurrent Events and Random Walks	p. 379
Recurrent Events-the Renewal Process	p. 379
Renewal Statistics	p. 396
Patterns in Bernoulli Trials	p. 417
Random Walks	p. 435
Birth and Death Processes	p. 446
Ruin Problems	p. 455
Markovian Population Models	p. 469
The Vector Markov Process	p. 469
Branching Processes	p. 490
Time-Varying Markov Processes	p. 511
The Chapman-Kolmogorov Equations	p. 511
Time-Varying Markov Process Examples	p. 516
Inverse Markov Processes	p. 525
Notation	p. 543
Appendixes
Properties of Congruent Matrix Multiplication	p. 549
A Paper	p. 551
References
Index	p. I-1
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