Recent Advances in Applied Probability

Contents......Page 6
Preface......Page 12
Acknowledgments......Page 14
1.1 Introduction......Page 16
1.2 Modeling a Document......Page 18
1.3 Relating the Heaps’ and Zipf’s Law......Page 22
1.4 Modeling a Document Collection......Page 23
1.5 Models for Queries and Answers......Page 25
1.6 Application: Inverted Files for the Web......Page 29
1.7 Concluding Remarks......Page 35
Appendix......Page 36
References......Page 39
2.1 Introduction......Page 42
2.2 Probabilistic models for finance......Page 43
2.3 Time series models......Page 53
2.4 Applications of time series to financial models......Page 61
References......Page 70
Stereological estimation of the rose of directions from the rose of intersections......Page 80
3.1 An analytical approach......Page 81
3.2 Convex geometry approach......Page 88
References......Page 110
4.1 Introduction......Page 112
4.2 The One Dimensional Case......Page 113
4.3 The Two Dimensional Case......Page 116
4.4 Numerical Results......Page 119
4.5 Concluding Remarks......Page 121
References......Page 128
5.1 What are Krawtchouk matrices......Page 130
5.2 Krawtchouk matrices from Hadamard matrices......Page 133
5.3 Krawtchouk matrices and symmetric tensors......Page 137
5.4 Ehrenfest urn model......Page 141
5.5 Krawtchouk matrices and classical random walks......Page 144
5.6 “Kravchukiana” or the World of Krawtchouk Polynomials......Page 148
5.7 Appendix......Page 152
References......Page 155
An Elementary Rigorous Introduction to Exact Sampling......Page 158
6.1 Introduction......Page 159
6.2 Exact Sampling......Page 163
6.3 Monotonicity......Page 172
6.4 Random Fields and the Ising Model......Page 174
6.5 Conclusion......Page 175
References......Page 176
7.1 Introduction......Page 178
7.2 Basics......Page 179
7.3 The theorem and its extensions......Page 185
7.4 Explicit expressions of the entropy rate......Page 190
References......Page 192
Dynamic stochastic models for indexes and thesauri, identification clouds,and information retrieval and storage......Page 196
8.1 Introduction......Page 197
8.2 A First Preliminary Model for the Growth of Indexes......Page 198
8.3 A Dynamic Stochastic Model for the Growth of Indexes......Page 200
8.4 Identification Clouds......Page 201
8.5 Application 1: Automatic Key Phrase Assignment......Page 203
8.6 Application 2: Dialogue Mediated Information Retrieval......Page 206
8.8 Application 4: Disambiguation......Page 207
8.9 Application 5. Slicing Texts......Page 208
8.10 Weights......Page 209
8.12 Application 7. Crosslingual IR......Page 211
8.14 Application 9. Formula Recognition......Page 212
8.16 Models for ID Clouds......Page 214
8.18 Multiple Identification Clouds......Page 215
8.19 More about Weights. Negative Weights......Page 216
8.20 Further Refinements and Issues......Page 217
References......Page 218
9.1 Introduction......Page 220
9.2 Stability conditions for semi-Markov systems......Page 223
9.3 Optimization of continuous control systems with semi-Markov coefficients......Page 226
9.4 Optimization of discrete control systems with semi-Markov coefficients......Page 231
References......Page 236
10.1 Introduction and background......Page 238
10.2 The nearest neighbor  Φ-divergence and main results......Page 241
10.3 Statistical distances based on Voronoi cells......Page 246
10.4 The objective method......Page 248
References......Page 253
11.1 Introduction......Page 256
11.2 Probabilistic Interpretation......Page 259
11.3 Statics......Page 267
11.4 Dynamics......Page 278
References......Page 282
12.1 Introduction......Page 284
12.3 Results......Page 286
12.4 Proofs......Page 288
Appendix......Page 292
References......Page 293
13.1 Introduction......Page 294
13.2 Preliminaries......Page 297
13.3 Increment Process......Page 298
13.4 Increment Process in an Asymptotic Split Phase Space......Page 301
13.5 Continuous Additive Functional......Page 305
13.6 Scheme of Proofs......Page 307
References......Page 311
14.1 Introduction......Page 314
14.2 Penalized model selection......Page 316
14.3 Minimax estimation for ill posed problems......Page 318
14.4 Penalized model selection for ill posed linear problems......Page 321
14.5 Bayesian interpretation......Page 326
14.6 L[sup(1)] penalization......Page 328
14.7 Numerical examples......Page 329
14.8 Appendix......Page 332
References......Page 341
15.1 Introduction......Page 344
15.2 Notations and preliminaries......Page 345
15.3 Levinson’s Algorithm and Schur’s Algorithm......Page 348
15.4 The Christoffel-Darboux formula......Page 350
15.5 Description of all spectrums of a stationary process......Page 351
15.6 On covariance’s extension problem......Page 357
15.7 Burg’s Entropy......Page 361
References......Page 363
16.1 Introduction......Page 366
16.2 Notation and Background Material......Page 368
16.3 The geometry of small balls and tubes......Page 376
16.4 Spectral Geometry......Page 380
16.5 Isoperimetric Conditions and Comparison Geometry......Page 390
16.6 Minimal Varieties......Page 397
16.7 Harmonic Functions......Page 398
16.8 Hodge Theory......Page 403
References......Page 406
Dependence or Independence of the Sample Mean and Variance In Non-IID or Non-Normal Cases and the Role or Some Tests of Independence......Page 412
17.1 Introduction......Page 413
17.2 A Multivariate Normal Probability Model......Page 420
17.4 Bivariate Non-Normal Probability Models: Case I......Page 421
17.5 Bivariate Non-Normal Probability Models: Case II......Page 427
17.6 A Bivariate Non-Normal Population: Case III......Page 433
17.7 Multivariate Non-Normal Probability Models......Page 437
17.8 Concluding Thoughts......Page 439
Acknowledgments......Page 440
References......Page 441
18.1 Introduction......Page 442
18.2 Formulation of the problem......Page 445
18.3 Excessive and superharmonic functions......Page 446
18.4 Characterization of the value function......Page 448
18.5 The free-boundary problem and the principle of smooth fit......Page 451
18.6 Examples and applications......Page 456
References......Page 467
19.1 Introduction......Page 470
19.2 Basic epidemiological model......Page 471
19.3 Measles around criticality......Page 473
19.4 Meningitis around criticality......Page 479
19.5 Spatial stochastic epidemics......Page 487
19.6 Directed percolation and path integrals......Page 497
19.7 Summary......Page 505
References......Page 506
I......Page 510
V......Page 511
Z......Page 512