This unique text collects more than 400 problems in combinatorics,
derived distributions, discrete and continuous Markov chains, and
models requiring a computer experimental approach. The first book
to deal with simplified versions of models encountered in the
contemporary statistical or engineering literature, Algorithmic
Probability emphasizes correct interpretation of numerical results
and visualization of the dynamics of stochastic processes.
A significant contribution to the field of applied probability,
Algorithmic Probability is ideal both as a secondary text in
probability courses and as a reference. Engineers and operations
analysts seeking solutions to practical problems will find it a
valuable resource, as will advanced undergraduate and graduate
students in mathematics, statistics, operations research, industrial
and electrical engineering, and computer science.
Author(s): Marcel F. Neuts
Series: Stochastic Modeling Series 3
Publisher: Chapman & Hall
Year: 1995
Language: English
Pages: 478
Neuts M.F. Algorithmic Probability_A Collection of Problems (Stochastic Modeling Series book 3)(C&H, 1995)(ISBN 041299691X)(600dpi)(478p) ......Page 4
Copyright ......Page 5
Table of Contents v ......Page 6
Preface ix ......Page 9
1.1. An Historical Perspective 1 ......Page 13
1.2. Recognizing Recurrence Relations 3 ......Page 15
Easier Problems 15 ......Page 27
Average Problems 19 ......Page 31
Harder Problems 25 ......Page 37
Challenging Problems 32 ......Page 44
Some Special Problems 36 ......Page 48
2.1. Common Equations 38 ......Page 50
2.2. Implicit Equations 43 ......Page 55
Easier Problems 46 ......Page 58
Average Problems 51 ......Page 63
Harder Problems 56 ......Page 68
Challenging Problems 66 ......Page 78
3.1. Introduction 75 ......Page 87
3.2. Sums of Random Variables 78 ......Page 90
3.3. Maxima and Minima of Random Variables 82 ......Page 94
3.4. The Inclusion - Exclusion Formula 85 ......Page 97
3.5. A Waiting Time in Multinomial Trials 88 ......Page 100
Easier Problems 92 ......Page 104
Average Problems 98 ......Page 110
Harder Problems 105 ......Page 117
Challenging Problems 117 ......Page 129
Problems Requiring Numerical Integration 128 ......Page 140
Problems on Inclusion - Exclusion 133 ......Page 145
4.1. Matrix Formulas for Finite Markov Chains 135 ......Page 147
4.2. Some Infinite-State Markov Chains 144 ......Page 156
4.3. The Discrete Markovian Arrival Process 149 ......Page 161
4.4. Main Problem Set for Chapter 4 153 ......Page 165
Easier Problems 154 ......Page 166
Average Problems 166 ......Page 178
Harder Problems 189 ......Page 201
Challenging Problems 207 ......Page 219
5.1. Matrix Formulas for Finite Markov Chains 229 ......Page 241
5.2. Main Problem Set for Chapter 5 237 ......Page 249
Easier Problems 238 ......Page 250
Average Problems 245 ......Page 257
Harder Problems 255 ......Page 267
Challenging Problems 272 ......Page 284
6.1. Introduction 292 ......Page 304
6.2. The Alias Method 296 ......Page 308
6.3. Understanding Steady-State Behavior 298 ......Page 310
Easier Problems 303 ......Page 315
Average Problems 309 ......Page 321
Harder Problems 332 ......Page 344
Challenging Problems 355 ......Page 367
References 367 ......Page 379
A. 1.1: Functions of a Matrix 369 ......Page 381
A. 1.2: The Kronecker Product 373 ......Page 385
A. 1.3: The Perron - Frobenius Eigenvalue 374 ......Page 386
A.2.1: PH -Distributions 379 ......Page 391
A.2.2: The PH -Renewal Process 388 ......Page 400
A.3.1: Description of the MAP 393 ......Page 405
A.3.2: Probability Distributions for the MAP 395 ......Page 407
Solutions to Selected Problems 399 ......Page 411
Index 459 ......Page 471
cover......Page 1
