Stochastic processes : theory and methods:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2001
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Handbook of statistics
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 967 S.: graph. Darst. |
| ISBN: | 0444500146 |
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Datensatz im Suchindex
| _version_ | 1804128470702227456 |
|---|---|
| adam_text | Table of contents
Preface v
Contributors xv
Ch. 1. Pareto Processes 1
Barry C. Arnold
1. Introduction 1
2. Distributional properties of Pareto variables 2
3. Multivariate Pareto distributions 4
4. Pareto processes 11
5. Autoregressive classical Pareto processes 12
6. Autoregressive Pareto (III) processes 16
7. Extensions and modifications 22
8. Related processes 27
References 32
Ch. 2. Branching Processes 35
K. B. Athreya and A. N. Vidyashankar
1. Introduction 35
2. Branching processes: Single type case 36
3. Branching process: Multitype case 40
4. Continuous time (age dependent) branching processes 44
5. Branching processes in random environments 46
6. Branching random walks 48
Acknowledgements 50
References 50
Ch. 3. Inference in Stochastic Processes 55
/. V. Basawa
1. Introduction 55
2. Likelihood methods 56
vii
viii Table of contents
3. Optimal estimating functions 66
4. Semiparametric models and adaptive estimation 67
5. Bayes and empirical Bayes methods 68
6. Some applications 69
Acknowledgement 75
References 76
Ch. 4. Topics in Poisson Approximation 79
A. D. Bar bow
1. Introduction 79
2. The Stein Chen method 84
3. Probabilities of small counts 91
4. Poisson point process approximation 96
5. Compound Poisson approximation 103
Acknowledgement 112
References 112
Ch. 5. Some Elements on Levy Processes 117
Jean Bertoin
1. Introduction 117
2. Basic aspects of Levy processes 118
3. Distribution of some functionals 127
4. Some sample path properties 135
References 142
Ch. 6. Iterated Random Maps and Some Classes of Markov Processes 145
Rabi Bhattacharya and Edward C. Waymire
1. Introduction 145
2. Ergodic problem, rates of convergence, and the central limit theorem 154
3. Doeblin s minorization and coupling via backward iteration 155
4. Harris recurrence, small sets, local minorization, and regeneration 157
5. Liapounov functionals and Foster Tweedie drift conditions 158
6. Dubins Freedman splitting for monotone maps and its generalization 159
7. Localized splitting 162
8. Examples revisited 165
Acknowledgements 168
References 168
Table of contents ix
Ch. 7. Random Walk and Fluctuation Theory 171
N. H. Bingham
Part I: Random walk on Euclidean space 171
1. Introduction 171
2. Simple random walk on 2 171
3. Recurrence and transience 173
4. Simple random walk on Z ; Polya s theorem 174
5. Random walks on W1 175
6. Harmonic analysis 177
7. Potential theory 177
8. Coupling 179
9. Renewal theory 179
10. Limit theorems and Brownian motion 180
11. Conditioned random walks 181
Part II: Random walks in more general contexts 182
1. Random walks and electrical networks 182
2. Random walk on graphs 183
3. Random walks on groups 185
4. Brownian motion on Riemannian manifolds 188
5. Random walks on homogeneous spaces, Gelfand pairs,
hypergroups and semigroups 189
6. Random walk on graphs with special structure 190
7. Variants on random walk 191
Part III: Fluctuation theory 193
1. Spitzer s identity 193
2. Ladder epochs and heights 195
3. Spitzer s arc sine law 197
4. Ballot theorems 199
5. Queues 199
6. Continuous time 201
7. Barrier problems 203
8. Higher dimensions and algebraic extensions 204
9. Distribution free results and non parametric statistics 205
10. Postscript 206
References 206
Ch. 8. A Semigroup Representation and Asymptotic Behavior of
Certain Statistics of the Fisher Wright Moran Coalescent 215
Adam Bobrowski, March Kimmel, Ovule Arino and Ranajit Chakrahortv
1. Introduction 215
2. Markov chain mutations and genetic drift in populations of varying size 217
3. Mathematical preliminaries 219
4. The Lyapunov equation and its asymptotic behavior 222
5. Stepwise Mutation Model with variable population size 235
6. Discussion 240
7. Acknowledgements 242
8. Appendix 242
References 246
x Table of contents
Ch. 9. Continuous Time ARMA Processes 249
P. J. Brockwell
1. Introduction 249
2. CARMA (p, q) processes 251
3. ARMA (p.q) processes 256
4. Embedding and aliasing 259
5. Inference for linear CARMA processes 263
6. Nonlinear CAR models 264
7. CTAR (p) processes 267
8. Inference for CTAR processes 270
Acknowledgement 275
References 275
Ch. 10. Record Sequences and their Applications 277
John Bunge and Charles M. Goldie
1. Introduction 277
2. Partial records 278
3. Record values 280
4. Sojourns 284
5. Record times 289
6. Limit theory and strong approximation 292
7. Extensions, connections and applications 295
8. Random record processes 298
9. Poisson paced records 299
10. Birth process paced records 301
11. Renewal paced records 303
12. Extensions and applications 306
References 306
Ch. 11. Stochastic Networks with Product Form Equilibrium 309
Hans Daduna
1. Introduction 309
2. Birth death processes and exponential networks of queues 311
3. Vector valued birth death processes and generalized migration processes 317
4. Migration processes with concurrent movements and
an application of local balance principles 322
5. Stochastic ordering and stochastic comparison for network processes 327
6. Correlation theory for network processes 330
7. Customers of different types, the arrival theorem 334
8. Individual customers sojourn time distributions and passage time distributions 339
9. General and symmetric servers: Insensitivity theory 346
10. Mixed networks of general exponential and symmetric servers 354
11. Complements 357
References 359
Table of contents xi
Ch. 12. Stochastic Processes in Insurance and Finance 365
Paul Embrechts, Riidiger Frey and Hansjorg Furrer
1. Introduction 365
2. Stochastic processes in insurance 373
3. Stochastic processes in finance 389
4. On the interplay between finance and insurance 404
Acknowledgements 408
References 408
Ch. 13. Renewal Theory 413
D. R. Grey
1. Introduction 413
2. Feller s recurrent events 414
3. Theorems of Blackwell. Feller and Orey 418
4. Renewal equations 420
5. Markov renewal and semi regenerative processes 424
6. Kingman s regenerative phenomena 425
7. Superposition of renewal processes 427
8. Applications to random walks and branching processes 429
9. An inventory model 432
10. Stationary increments 434
11. Goldie s implicit renewal theory 436
12. Schmidli s extension 439
References 440
Ch. 14. The Kolmogorov Isomorphism Theorem and Extensions to
some Nonstationary Processes 443
Yiuchiro Kakihara
1. Introduction 443
2. Stationary processes and the Kolmogorov Isomorphism Theorem 444
3. Some classes of nonstationary processes 447
4. Weakly harmonizable processes and the Kolmogolov Isomorphism Theorem 453
5. Application to estimation and filtering 455
6. Multidimensional extension 460
Acknowledgement 468
References 468
Ch. 15. Stochastic Processes in Reliability 471
Masaaki Kijima, Haijim Li and Moshe Shaked
1. Introduction 471
2. Aging first passage times 472
xii Table of contents
3. Comparison of replacement policies via point processes 483
4. Comparison of repairable systems via point processes 495
5. A stochastic process approach to failure models in random environments 498
References 507
Ch. 16. On the supports of Stochastic Processes of Multiplicity One 511
A. Klopotowski and M. G. Nadkarni
0. Introduction 511
1. Additive decompositions, good sets 512
2. Graphs, couples and their unions 515
3. Links, linked and uniquely linked sets, loops 517
4. Orthogonal decompositions 522
5. Connection with dynamics, twisted joinings 525
6. Application to the problem of simple Lebesgue spectrum 526
7. Walsh functions 527
Acknowledgements 530
References 531
Ch. 17. Gaussian Processes: Inequalities, Small Ball Probabilities and
Applications 533
W. V. Li and Q. M. Shao
1. Introduction 533
2. Inequalities for Gaussian random elements 536
3. Small ball probabilities in general setting 543
4. Gaussian processes with index set T C R 556
5. Gaussian processes with index set TC R , d 2 563
6. The small ball constants 566
7. Applications of small ball probabilities 576
Acknowledgements 591
References 592
Ch. 18. Point Processes and Some Related Processes 599
Robin K. Milne
1. Introduction 599
2. Foundations 601
3. Operations on point processes and associated limit results 618
4. Some other classes of point process 622
5. Statistical inference 631
6. Simulation 635
7. Concluding remarks 636
Acknowledgements 637
References 638
Table of contents xiii
Ch. 19. Characterization and Identifiability for Stochastic Processes 643
B. L. S. Prakasa Rao
1. Introduction 643
2. Characterizations by properties of stochastic integrals of processes with
independent increments 644
3. Martingales and conditional structure characterizations 663
4. Characterizations for Poisson process as a renewal process and as a point process 675
5. Miscellaneous characterizations 684
Acknowledgement 687
References 687
Ch. 20. Associated Sequences and Related Inference Problems 693
B. L. S. Prakasa Rao and Isha Dew an
1. Introduction 693
2. Some probabilistic properties for associated sequences 704
3. Random generation of associated sequences 719
4. Statistical inference for associated sequences 720
References 728
Ch. 21. Exchangeability, Functional Equations, and Characterizations 733
C. R. Rao and D. N. Shanbhag
1. Introduction 733
2. de Finetti s theorem and some related auxiliary results 735
3. Functional equations with applications in probability and statistics 742
4. Characterizations of mixtures of probability distributions 755
Acknowledgement 761
References 761
Ch. 22. Martingales and Some Applications 765
M. M. Rao
1. Introduction 765
2. Martingale concepts and inequalities 767
3. Convergence theorems 773
4. Elements of (semi)martingale calculus 778
5. An application to likelihood ratios 793
6. Exponential (semi)martingales 797
7. Applications to financial market models 803
8. Remarks on multiparameter and other extensions 812
References 815
xiv Table of contents
Ch. 23. Markov Chains: Structure and Applications 817
R. L. Tweedie
1. Introduction 817
2. Countable space chains 820
3. General state space chains 831
4. Topological spaces 843
5. Conclusions 848
Acknowledgement 849
References 849
Ch. 24. Diffusion Processes 853
S. R. S. Varadhan
1. Brownian motion 853
2. Brownian motion as a Markov process 855
3. Semigroups and generators 856
4. Stochastic integrals 858
5. Ito calculus 859
6. Brownian motion with a drift 861
7. One dimensional diffusions 863
8. The multidimensional case 868
9. Diffusions with reflection 871
References 872
Ch. 25. Ito s Stochastic Calculus and Its Applications 873
S. Watanabe
0. Introduction 873
1. Semimartingales and stochastic integrals 874
2. Stochastic calculus for semimartingales 886
3. Stochastic differential equations 901
4. Stochastic differential equations on manifolds 920
References 931
Subject Index 935
Contents of Previous Volumes 947
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| spelling | Stochastic processes : theory and methods ed. by D. N. Shanbhag ... 1. ed. Amsterdam [u.a.] Elsevier 2001 XVII, 967 S.: graph. Darst. txt rdacontent n rdamedia nc rdacarrier Handbook of statistics 19 Processus stochastiques Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 Shanbhag, Dayanand N. Sonstige oth Handbook of statistics 19 (DE-604)BV000002510 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009333052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Stochastic processes : theory and methods |
| title_auth | Stochastic processes : theory and methods |
| title_exact_search | Stochastic processes : theory and methods |
| title_full | Stochastic processes : theory and methods ed. by D. N. Shanbhag ... |
| title_fullStr | Stochastic processes : theory and methods ed. by D. N. Shanbhag ... |
| title_full_unstemmed | Stochastic processes : theory and methods ed. by D. N. Shanbhag ... |
| title_short | Stochastic processes : theory and methods |
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