Stochastic processes : modelling and simulation:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2003
|
| Edition: | 1. ed. |
| Series: | Handbook of statistics
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 1000 S. graph. Darst. |
| ISBN: | 0444500138 |
Staff View
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| 245 | 1 | 0 | |a Stochastic processes : modelling and simulation |c ed. by D. N. Shanbhag ... |
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| 490 | 1 | |a Handbook of statistics |v 21 | |
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Record in the Search Index
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| adam_text | Table of contents
Preface v
Contributors xv
Ch. 1. Modelling and Numerical Methods in Manufacturing System Using Control
Theory 1
E. K. Boukas and Z. K. Liu
1. Introduction 1
2. Controlled piecewise deterministic processes 3
3. Continuous flow model for production control 15
4. Preventive maintenance and production control model 19
5. Maintenance model without considering the machine aging 32
6. Robust controller for a class of production and maintenance 36
7. Conclusion 46
References 47
Ch. 2. Models of Random Graphs and their Applications 51
C. Cannings and D. B. Penman
1. Introduction 51
2. Overview of the Erdos-Renyi model 57
3. Applications of the Erdos-Renyi model 63
4. Geometric random graphs 65
5. Random cluster models 69
6. Random randomly coloured graphs 72
7. Other models of random graphs 78
References 87
vii
viii Table of contents
Ch. 3. Locally Self-Similar Processes and their Wavelet Analysis 93
J. E. Cavanaugh, Y. Wang and J. W. Davis
1. Introduction 93
2. Locally self-similar processes 95
3. Generalized fractional Brownian motion 97
4. Estimating the scaling function 102
5. Implementation of the estimation procedure 104
6. Simulations 106
7. Applications 117
8. Conclusion 124
Appendix 124
References 133
Ch. 4. Stochastic Models for DNA Replication 137
R. Cowan
1. Variation in biology 137
2. Stochastic chemistry 138
3. Exponentially distributed waiting times 141
4. The biological cell 142
5. A glib mathematical abstraction 143
6. The spatial pattern of replication origins 144
7. The time to separation of a long DNA molecule 146
8. The proportion of origins initiated 150
9. Mean eye lengths and eye-to-eye distances 151
10. What is happening inside the eyes? 153
11. The Cowan-Chiu model of fragment formation 155
12. The expectations of Nt and Pt: renewal equations 155
13. The expectation of Dt: the quasi-renewal equation 157
14. Relationship between fragment length and primer-site spacing 159
15. Estimated spacing between primer sites 160
16. The competing theory 160
17. Notations for the competing theory 161
18. Analysis of the lagging strand for Model B 162
19. Analysis of the leading strand for Model B 163
20. Concluding remarks 164
References 165
Ch. 5. An Empirical Process with Applications to Testing the Exponential and
Geometric Models 167
J. A. Ferreira
1. Introduction 167
2. The empirical integrated lack-of-memory process 170
3. Connection with certain test statistics and empirical processes 172
4. Asymptotic behaviour of the process 181
5. Statement of results; examples and comparisons 190
6. Integral statistics. Applications to testing 196
Table of contents ix
7. Asymptotic efficiency in the continuous case 207
Acknowledgements 223
References 223
Ch. 6. Patterns in Sequences of Random Events 227
J. Gani
1. Early encounters: random numbers and the theory of runs 227
2. Sequences of events with repetitions 230
3. Strings and string overlaps 232
4. Further classical and martingale methods 235
5. Markov chain techniques 238
References 240
Ch. 7. Stochastic Models in Telecommunications for Optimal Design, Control and
Performance Evaluation 243
N. Gautam
1. Introduction 243
2. Traffic models 244
3. Network performance using traffic models 250
4. LAN (multiaccess communication) models 268
5. Other topics and models 272
Acknowledgements 280
References 281
Ch. 8. Stochastic Processes in Epidemic Modelling and Simulation 285
D. Greenhalgh
1. Introduction 285
2. Chain binomial models 285
3. The simple and general stochastic epidemic models 288
4. Spatial models 301
5. Stochastic models for control of epidemics 308
6. Specific applications 312
7. Stochastic processes in parameter estimation and hypothesis testing 321
8. Summary and conclusions 328
Acknowledgement 330
References 330
x Table of contents
Ch. 9. Empirical Estimators Based on MCMC Data 337
P. E. Greenwood and W. Wefelmeyer
1. Introduction 337
2. The asymptotic variance of empirical estimators for Markov chains 341
3. Efficient estimation for Markov chain models 345
4. Improving empirical estimators by conditioning 348
5. Asymptotic variance of empirical estimators for Gibbs samplers 351
6. Asymptotic variance bounds for Gibbs samplers 353
7. Improving empirical estimators for random fields with local interactions 359
8. Exploiting symmetries of random fields 363
Acknowledgement 366
References 366
Ch. 10. Fractals and the Modelling of Self-Similarity 371
B. M. Hambly
1. Introduction 371
2. Fractal geometry 373
3. Fractals and stochastic processes 388
4. Dynamic fractal models 391
5. Further applications and conclusion 403
References 404
Ch. 11. Numerical Methods in Queueing Theory 407
D. Heyman
1. Introduction 407
2. Numerical inversion of Laplace transforms 410
3. The ubiquity of Markov chains 413
4. Finite Markov chains 414
5. Infinite Markov chains 418
6. The BMAP/G/1 queue 423
7. The quasi birth-and-death process 425
References 428
Ch. 12. Applications of Markov Chains to the Distribution Theory of Runs and
Patterns 431
M. V. Koutras
1. Introduction 431
2. The Markov Chain imbedding technique 433
3. Success runs and pattern distributions 435
4. Markov Chain imbeddable variables of binomial type 443
5. Waiting time distributions associated with MVB s 446
6. The number of runs and patterns as members of the MVB family 448
7. Multivariate MVB distributions 454
Table of contents xi
8. Multivariate success runs distributions 457
9. Alternative methods for exact distribution evaluation 466
References 470
Ch. 13. Modelling Image Analysis Problems Using Markov Random Fields 473
S. Z. Li
1. Introduction 473
2. Image labeling 475
3. Markov random fields and Gibbs distributions 480
4. Useful MRF models 489
5. The MAP-MRF framework 499
Acknowledgement 507
References 507
Ch. 14. An Introduction to Semi-Markov Processes with Application to
Reliability 515
N. Limnios and G. Opri§an
1. Introduction 515
2. Semi-Markov kernel 516
3. Markov renewal processes (MRP) 518
4. Semi-Markov processes with an arbitrary state space 525
5. Markov renewal equation 528
6. The countable case 532
7. Classification of states 537
8. Asymptotic behavior 540
9. Some recent approaches to semi-Markov processes 542
10. Reliability modeling and estimation 551
References 554
Ch. 15. Departures and Related Characteristics in Queueing Models 557
M. Manoharan, M. H. Alamatmz and D. N. Shanbhag
1. Introduction 557
2. Characterization/identitiability via output processes 558
3. Characterization/identifiability via infinite divisibility property 564
4. Strong unimodality and other relevant properties 568
References 570
xii Table of contents
Ch. 16. Discrete Variate Time Series 573
E. McKenzie
1. Introduction 573
2. Markov chains 575
3. The DARMA models 576
4. Models based on thinning 578
5. Regression models 594
6. State space and Bayesian models 597
7. The future 602
References 602
Ch. 17. Extreme Value Theory, Models and Simulation 607
S. Nadarajah
1. Introduction 607
2. Limit laws in univariate extremes and characterizations 608
3. Rates of convergence 613
4. Generalized extreme value (GEV) distribution 618
5. Generalized Pareto (GP) distribution 620
6. Joint distribution of the r-largest order statistics 623
7. A point process characterization 624
8. Extremes of stochastic processes 625
9. Limit laws for multivariate extremes 635
10. Characterizations of the domain of attraction 637
11. Characterizations of multivariate extreme value distributions 649
12. Rates of convergence 652
13. Parametric families for bivariate extreme value distributions 654
14. Parametric families for multivariate extreme value distributions 663
15. Extremes of multivariate stochastic processes 677
Acknowledgements 679
References 680
Ch. 18. Biological Applications of Branching Processes 693
A. G. Pakes
0. Introduction 693
1. History, surnames, and sex 695
2. Genetics and evolution 703
3. Epidemic modelling 728
4. Ecology and conservation modelling 738
References 762
Table of contents xiii
Ch. 19. Markov Chain Approaches to Damage Models 775
C. R. Rao, M. Albassam, M. B. Rao and D. N. Shanbhag
1. Introduction 775
2. Modified versions of some basic results on damage models 776
3. Characterizations based on modified Rao-Rubin conditions 782
4. Characterization via conditional expectations 788
References 793
Ch. 20. Point Processes in Astronomy: Exciting Events in the Universe 795
J. D. Scargle and G. J. Babu
1. Introduction: what s the point? 795
2. Unique features of astronomical point processes 797
3. Naive point process theory 798
4. The mystery of Gamma Ray bursts 801
5. Other examples of astronomical point processes 815
6. Conclusion 822
Acknowledgement 823
References 823
Ch. 21. On the Theory of Discrete and Continuous Bilinear Time Series Models 827
T. Subba Rao and Gy. Terdik
1. Introduction 827
2. Linear time series models and cumulant spectra 833
3. Volterra expansion and bilinear models 834
4. Higher-order moments and identification 837
5. Estimation of higher-order cumulants and the bilinear models 838
6. Multivariate nonlinear time series and higher-order cumulants of random vectors 843
7. Spurious regression and cointegration. nonlinearity 847
8. Time dependent nonlinear models 850
9. Long range dependence 852
10. Stationary bilinear process in continuous time 861
Acknowledgement 866
References 867
Ch. 22. Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo
Techniques: A Survey and Comparative Study 871
H. Tanizaki
1. Introduction 871
2. State-space model 874
3. Nonlinear and non-Gaussian state-space modeling 887
4. Monte Carlo studies 906
5. Summary and concluding remarks 917
Appendix A. Linear and normal system 919
xiv Table of contents
Appendix B. Sampling methods 920
Appendix C. Recursive versus non-recursive algorithms 923
Acknowledgements 926
References 926
Ch. 23. Markov Modelling of Burst Behaviour in Ion Channels 931
G. F. Yeo, R. K. Milne, B. W. Madsen, Y Li and R. O. Edeson
1. Introduction 931
2. Aggregated Markov chains 934
3. Theoretical bursts 939
4. Empirical bursts 945
5. A five-state ligand-activated ion channel model 949
6. A linear sequential model with drug blockade 951
7. A model showing biphasic drug effects 955
8. A model for a supergated double-barrelled chloride channel 958
9. Some comments on statistical inference 963
Note added in proof 964
Acknowledgements 965
References 965
Subject Index 969
Contents of Previous Volumes 979
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| spelling | Stochastic processes : modelling and simulation ed. by D. N. Shanbhag ... 1. ed. Amsterdam [u.a.] Elsevier 2003 XVII, 1000 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Handbook of statistics 21 Modèles mathématiques Processus stochastiques Simulatie gtt Simulation par ordinateur Stochastische processen gtt Wiskundige modellen gtt Mathematisches Modell Computer simulation Mathematical models 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 21 (DE-604)BV000002510 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010245372&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 |
| spellingShingle | Stochastic processes : modelling and simulation Handbook of statistics Modèles mathématiques Processus stochastiques Simulatie gtt Simulation par ordinateur Stochastische processen gtt Wiskundige modellen gtt Mathematisches Modell Computer simulation Mathematical models Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4143413-4 |
| title | Stochastic processes : modelling and simulation |
| title_auth | Stochastic processes : modelling and simulation |
| title_exact_search | Stochastic processes : modelling and simulation |
| title_full | Stochastic processes : modelling and simulation ed. by D. N. Shanbhag ... |
| title_fullStr | Stochastic processes : modelling and simulation ed. by D. N. Shanbhag ... |
| title_full_unstemmed | Stochastic processes : modelling and simulation ed. by D. N. Shanbhag ... |
| title_short | Stochastic processes : modelling and simulation |
| title_sort | stochastic processes modelling and simulation |
| topic | Modèles mathématiques Processus stochastiques Simulatie gtt Simulation par ordinateur Stochastische processen gtt Wiskundige modellen gtt Mathematisches Modell Computer simulation Mathematical models Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Modèles mathématiques Processus stochastiques Simulatie Simulation par ordinateur Stochastische processen Wiskundige modellen Mathematisches Modell Computer simulation Mathematical models Stochastic processes Stochastischer Prozess Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010245372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002510 |
| work_keys_str_mv | AT shanbhagdayanandn stochasticprocessesmodellingandsimulation |