Discrete stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer
1996
|
| Schriftenreihe: | The Kluwer international series in engineering and computer science
321 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 271 S. graph. Darst. |
| ISBN: | 0792395832 9780792395836 |
Internformat
MARC
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| 245 | 1 | 0 | |a Discrete stochastic processes |c by Robert G. Gallager |
| 264 | 1 | |a Boston [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XIII, 271 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a The Kluwer international series in engineering and computer science |v 321 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xi
Chapter 1 Introduction and Probability Review 1
1 1 Introduction 1
1 2 Probability Review 2
1 3 Conditional Probabilities 5
1 4 Random Variables 5
1 5 Expectations 8
1 6 Transforms 11
1 7 Weak Law of Large Numbers 12
Basic Inequalities 12
Weak Law Assuming a Finite Variance 14
The Central Limit Theorem 15
Relative Frequency and Indicator Functions 18
Weak Law with Infinite Variance 19
1 8 Strong Law of Large Numbers 21
1 9 Summary 25
Table of Standard Random Variables 25
Exercises 26
Notes 30
Chapter 2 Poisson Processes 31
2 1 Introduction 31
2 2 Definition and Properties of the Poisson Process 33
Memoryless Property 33
Distribution Functions for Sn and N(t) 35
2 3 Combinations and Subdivisions of Independent Poisson Processes 38
Subdividing a Poisson Process 39
Examples Using Independent Poisson Processes 41
2 4 Non-Homogeneous Poisson Processes 41
Example—The M/G/°° Queue 43
2 5 Order Statistics and Conditional Arrival Epochs 45
vii
viii Contents
2 6 Summary 48
Exercises 49
Notes 55
Chapter 3 Renewal Processes 57
3 1 Introduction 57
3 2 Strong Law of Large Numbers for Renewal Processes 58
Central Limit Theorem for N(t) 61
3 3 Expected Number of Renewals 62
Laplace Transform Approach 63
Wald’s Equality 64
Stopping Rules 65
The Elementary Renewal Theorem 67
Blackwell’s Theorem 68
3 4 Renewal Reward Processes; Time Averages 69
Time Average Residual Life 70
Time Average Age 72
Time Average Duration 73
General Renewal Reward Functions 74
Distribution of Residual Life 75
3 5 Renewal Reward Processes; Ensemble Averages 77
3 6 Applications of Renewal Reward Theory 81
Little’s Theorem 81
Expected Queueing Time for an M/G/l Queue 85
3 7 Delayed Renewal Processes 87
Strong Law for Delayed Renewal Processes 88
Elementary Delayed Renewal Theorem 89
Blackwell Theorem for Delayed Renewals 89
Delayed Renewal Reward Processes 90
Transient Behavior of Delayed Renewal Processes 90
Equilibrium Process 91
3 8 Summary 92
Exercises 92
Notes 101
Chapter 4 Finite State Markov Chains 103
4 1 Introduction 103
4 2 Classification of States 105
4 3 The Matrix Representation 109
Eigenvalues and Eigenvectors of P 111
4 4 Perron-Frobenius Theory 112
4 5 Markov Chains with Rewards 119
Expected First Passage Time 119
Contents ix
4 6 Markov Decision Theory and Dynamic Programming 126
Dynamic Programming Algorithm 127
Optimal Stationary Policy 129
Howard’s Policy Improvement Algorithm 132
4 7 Summary 136
Exercises 137
Notes 147
Chapter 5 Markov Chains with Countably Infinite State Spaces 149
5 1 Introduction and Classification of States 149
5 2 Branching Processes 158
5 3 Birth Death Markov Chains 160
5 4 Reversible Markov Chains 161
5 5 The M/M/1 Sampled Time Markov Chain 165
5 6 Round-Robin and Processor Sharing 168
5 7 Semi-Markov Processes 174
5 8 Example—M/G/l Queue 179
5 9 Summary 180
Exercises 181
Chapter 6 Markov Processes with Countable State Spaces 187
6 1 Introduction 187
Pathological Cases 191
6 2 The Kolmogorov Differential Equations 192
6 3 Uniformization 195
6 4 Birth Death Processes 196
6 5 Reversibility for Markov Processes 199
6 6 Jackson Networks 205
Closed Jackson Networks 211
6 7 Summary 213
Exercises 214
Chapter 7 Random Walks and Martingales 223
7 1 Introduction 223
Simple Random Walk 223
7 2 The G/G/l Queue 225
7 3 Detection, Decisions, and Hypothesis Testing 227
7 4 Threshold Crossing Probabilities 229
7 5 Wald’s Identity and Walks with Two Thresholds 232
Joint Distribution of N and Barrier 235
Proof of Wald’s Identity 236
7 6 Martingales and Submartingales 239
Zero Mean Random Walk 240
Sums of Dependent Zero Mean Variables 240
Product Form Martingales 240
Markov Modulated Random Walks 241
Generating Function for Markov Walk 243
Scaled Branching Processes 244
Submartingales and Supermartingales 245
Convex Functions of Martingales 246
7 7 Stopped Processes and Stopping Rules 247
Random Walks with Thresholds 250
Stopping Rules for Martingales Relative to a Process 251
Markov Modulated Random Walks with Thresholds 251
7 8 The Kolmogorov Inequalities 253
Strong Law of Large Numbers 255
Martingale Convergence Theorem 256
7 9 Summary 257
Exercises 258
Notes 263
Bibliography 265
|
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| id | DE-604.BV010644163 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:30Z |
| institution | BVB |
| isbn | 0792395832 9780792395836 |
| language | English |
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| physical | XIII, 271 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | The Kluwer international series in engineering and computer science |
| series2 | The Kluwer international series in engineering and computer science |
| spelling | Gallager, Robert G. Verfasser (DE-588)128058072 aut Discrete stochastic processes by Robert G. Gallager Boston [u.a.] Kluwer 1996 XIII, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Kluwer international series in engineering and computer science 321 Stochastic processes Diskreter stochastischer Prozess (DE-588)4150187-1 gnd rswk-swf Diskreter stochastischer Prozess (DE-588)4150187-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4615-2329-1 The Kluwer international series in engineering and computer science 321 (DE-604)BV023545171 321 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007102362&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallager, Robert G. Discrete stochastic processes The Kluwer international series in engineering and computer science Stochastic processes Diskreter stochastischer Prozess (DE-588)4150187-1 gnd |
| subject_GND | (DE-588)4150187-1 |
| title | Discrete stochastic processes |
| title_auth | Discrete stochastic processes |
| title_exact_search | Discrete stochastic processes |
| title_full | Discrete stochastic processes by Robert G. Gallager |
| title_fullStr | Discrete stochastic processes by Robert G. Gallager |
| title_full_unstemmed | Discrete stochastic processes by Robert G. Gallager |
| title_short | Discrete stochastic processes |
| title_sort | discrete stochastic processes |
| topic | Stochastic processes Diskreter stochastischer Prozess (DE-588)4150187-1 gnd |
| topic_facet | Stochastic processes Diskreter stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007102362&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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