Stochastic Processes: Modeling and Simulation

Pirmais vāks
D N Shanbhag, Calyampudi Radhakrishna Rao
Gulf Professional Publishing, 2003. gada 10. marts - 1000 lappuses

This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

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Saturs

Modelling and Numerical Methods in Manufacturing System Using Control
1
W Wefelmeyer Fachbereich 6 Mathematik Universität Siegen WalterFlexStr
3
N Gautam Department of Industrial and Manufacturing Engineering The Pennsyl
7
S Z Li Microsoft Research China 1 Beijing Sigma Center Beijing 100080 China
13
Continuous flow model for production control
15
G F Yeo Mathematics and Statistics DSE Murdoch University Murdoch 6150
23
Maintenance model without considering the machine aging
32
Conclusion
46
The BMAPG1 queue
423
Applications of Markov Chains to the Distribution Theory of Runs
431
Markov Chain imbeddable variables of binomial type
443
Multivariate MVB distributions
454
Modelling Image Analysis Problems Using Markov Random Fields
473
Markov random fields and Gibbs distributions
480
Useful MRF models
489
The MAPMRF framework
499

Overview of the ErdősRényi model
57
Applications of the ErdősRényi model
63
Random cluster models
69
Other models of random graphs
78
Locally SelfSimilar Processes and their Wavelet Analysis
93
Locally selfsimilar processes
95
Generalized fractional Brownian motion
97
Estimating the scaling function
102
Implementation of the estimation procedure
104
Simulations
106
Applications
117
Conclusion
124
References
133
Stochastic Models for DNA Replication
137
Stochastic chemistry
138
Exponentially distributed waiting times
141
The biological cell
142
A glib mathematical abstraction
143
The spatial pattern of replication origins
144
The time to separation of a long DNA molecule
146
The proportion of origins initiated
150
Mean eye lengths and eyetoeye distances
151
What is happening inside the eyes?
153
The CowanChiu model of fragment formation
155
the quasirenewal equation
157
Relationship between fragment length and primersite spacing
159
Estimated spacing between primer sites
160
Notations for the competing theory
161
Analysis of the lagging strand for Model B
162
Analysis of the leading strand for Model B
163
Concluding remarks
164
References
165
An Empirical Process with Applications to Testing the Exponential and Geometric Models
167
The empirical integrated lackofmemory process
170
Connection with certain test statistics and empirical processes
172
Asymptotic behaviour of the process
181
Statement of results examples and comparisons
190
Integral statistics Applications to testing
196
Asymptotic efficiency in the continuous case
207
Patterns in Sequences of Random Events
227
Further classical and martingale methods
235
Stochastic Models in Telecommunications for Optimal Design Control
243
Network performance using traffic models
250
LAN multiaccess communication models
268
Stochastic Processes in Epidemic Modelling and Simulation
285
Spatial models
301
Stochastic models for control of epidemics
308
Stochastic processes in parameter estimation and hypothesis testing
321
Summary and conclusions
328
Empirical Estimators Based on MCMC Data
337
Efficient estimation for Markov chain models
345
Asymptotic variance of empirical estimators for Gibbs samplers
351
Improving empirical estimators for random fields with local interactions
359
Fractals and the Modelling of SelfSimilarity
371
Numerical Methods in Queueing Theory
407
The ubiquity of Markov chains
413
Ch 14
515
SemiMarkov processes with an arbitrary state space
525
The countable case
532
Asymptotic behavior
540
Reliability modeling and estimation
551
Departures and Related Characteristics in Queueing Models
557
Characterizationidentifiability via infinite divisibility property
564
Discrete Variate Time Series
573
Markov chains
575
The DARMA models
576
Models based on thinning
578
Regression models
594
State space and Bayesian models
597
The future
602
Extreme Value Theory Models and Simulation
607
Limit laws in univariate extremes and characterizations
608
Rates of convergence
613
Generalized extreme value GEV distribution
618
Generalized Pareto GP distribution
620
Joint distribution of the rlargest order statistics
623
A point process characterization
624
Extremes of stochastic processes
625
Limit laws for multivariate extremes
635
Characterizations of the domain of attraction
637
Characterizations of multivariate extreme value distributions
649
Rates of convergence
652
Parametric families for bivariate extreme value distributions
654
Parametric families for multivariate extreme value distributions
663
Extremes of multivariate stochastic processes
677
Acknowledgements
679
References
680
Biological Applications of Branching Processes
693
History surnames and sex
695
Genetics and evolution
703
Epidemic modelling
728
Ecology and conservation modelling
738
References
762
Markov Chain Approaches to Damage Models
775
Characterizations based on modified RaoRubin conditions
782
Characterization via conditional expectations
788
Ch 20
795
The mystery of Gamma Ray bursts
801
Other examples of astronomical point processes
815
Conclusion
822
Linear time series models and cumulant spectra
833
Multivariate nonlinear time series and higherorder cumulants of random vectors
843
Time dependent nonlinear models
850
Stationary bilinear process in continuous time
861
Ch 22
871
Nonlinear and nonGaussian statespace modeling
887
Monte Carlo studies
906
Summary and concluding remarks
917
Markov Modelling of Burst Behaviour in Ion Channels
931
Subject Index
969
Contents of Previous Volumes
979

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