| Preface |
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| Contributors |
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xv | |
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Modelling and Numerical Methods in Manufacturing System Using Control Theory |
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1 | (50) |
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1 | (2) |
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Controlled piecewise deterministic processes |
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3 | (12) |
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Continuous flow model for production control |
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15 | (4) |
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Preventive maintenance and production control model |
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19 | (13) |
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Maintenance model without considering the machine aging |
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32 | (4) |
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Robust controller for a class of production and maintenance |
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36 | (10) |
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46 | (5) |
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47 | (4) |
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Models of Random Graphs and their Applications |
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51 | (42) |
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51 | (6) |
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Overview of the Erdos--Renyi model |
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57 | (6) |
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Applications of the Erdos--Renyi model |
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63 | (2) |
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65 | (4) |
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69 | (3) |
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Random randomly coloured graphs |
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72 | (6) |
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Other models of random graphs |
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78 | (15) |
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87 | (6) |
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Locally Self-Similar Processes and their Wavelet Analysis |
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93 | (44) |
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93 | (2) |
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Locally self-similar processes |
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95 | (2) |
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Generalized fractional Brownian motion |
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97 | (5) |
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Estimating the scaling function |
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102 | (2) |
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Implementation of the estimation procedure |
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104 | (2) |
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106 | (11) |
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117 | (7) |
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124 | (13) |
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124 | (9) |
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133 | (4) |
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Stochastic Models for DNA Replication |
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137 | (30) |
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137 | (1) |
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138 | (3) |
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Exponentially distributed waiting times |
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141 | (1) |
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142 | (1) |
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A glib mathematical abstraction |
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143 | (1) |
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The spatial pattern of replication origins |
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144 | (2) |
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The time to separation of a long DNA molecule |
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146 | (4) |
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The proportion of origins initiated |
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150 | (1) |
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Mean eye lengths and eye-to-eye distances |
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151 | (2) |
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What is happening inside the eyes? |
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153 | (2) |
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The Cowan--Chiu model of fragment formation |
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155 | (1) |
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The expectations of Nt and Pt: renewal equations |
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155 | (2) |
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The expectation of Dt: the quasi-renewal equation |
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157 | (2) |
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Relationship between fragment length and primer-site spacing |
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159 | (1) |
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Estimated spacing between primer sites |
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160 | (1) |
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160 | (1) |
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Notations for the competing theory |
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161 | (1) |
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Analysis of the lagging strand for Model B |
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162 | (1) |
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Analysis of the leading strand for Model B |
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163 | (1) |
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164 | (3) |
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165 | (2) |
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An Empirical Process with Applications to Testing the Exponential and Geometric Models |
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167 | (60) |
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167 | (3) |
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The empirical integrated lack-of-memory process |
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170 | (2) |
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Connection with certain test statistics and empirical processes |
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172 | (9) |
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Asymptotic behaviour of the process |
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181 | (9) |
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Statement of results; examples and comparisons |
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190 | (6) |
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Integral statistics. Applications to testing |
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196 | (11) |
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Asymptotic efficiency in the continuous case |
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207 | (20) |
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223 | (1) |
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223 | (4) |
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Patterns in Sequences of Random Events |
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227 | (16) |
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Early encounters: random numbers and the theory of runs |
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227 | (3) |
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Sequences of events with repetitions |
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230 | (2) |
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Strings and string overlaps |
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232 | (3) |
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Further classical and martingale methods |
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235 | (3) |
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238 | (5) |
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240 | (3) |
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Stochastic Models in Telecommunications for Optimal Design, Control and Performance Evaluation |
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243 | (42) |
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243 | (1) |
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244 | (6) |
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Network performance using traffic models |
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250 | (18) |
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LAN (multiaccess communication) models |
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268 | (4) |
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272 | (13) |
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280 | (1) |
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281 | (4) |
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Stochastic Processes in Epidemic Modelling and Simulation |
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285 | (52) |
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285 | (1) |
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285 | (3) |
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The simple and general stochastic epidemic models |
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288 | (13) |
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301 | (7) |
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Stochastic models for control of epidemics |
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308 | (4) |
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312 | (9) |
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Stochastic processes in parameter estimation and hypothesis testing |
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321 | (7) |
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328 | (9) |
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330 | (1) |
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330 | (7) |
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Empirical Estimators Based on MCMC Data |
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337 | (34) |
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337 | (4) |
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The asymptotic variance of empirical estimators for Markov chains |
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341 | (4) |
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Efficient estimation for Markov chain models |
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345 | (3) |
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Improving empirical estimators by conditioning |
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348 | (3) |
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Asymptotic variance of empirical estimators for Gibbs samplers |
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351 | (2) |
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Asymptotic variance bounds for Gibbs samplers |
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353 | (6) |
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Improving empirical estimators for random fields with local interactions |
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359 | (4) |
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Exploiting symmetries of random fields |
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363 | (8) |
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366 | (1) |
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366 | (5) |
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Fractals and the Modelling of Self-Similarity |
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371 | (36) |
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371 | (2) |
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373 | (15) |
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Fractals and stochastic processes |
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388 | (3) |
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391 | (12) |
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Further applications and conclusion |
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403 | (4) |
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404 | (3) |
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Numerical Methods in Queueing Theory |
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407 | (24) |
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407 | (3) |
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Numerical inversion of Laplace transforms |
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410 | (3) |
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The ubiquity of Markov chains |
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413 | (1) |
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414 | (4) |
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418 | (5) |
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423 | (2) |
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The quasi birth-and-death process |
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425 | (6) |
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428 | (3) |
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Applications of Markov Chains to the Distribution Theory of Runs and Patterns |
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431 | (42) |
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431 | (2) |
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The Markov Chain imbedding technique |
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433 | (2) |
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Success runs and pattern distributions |
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435 | (8) |
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Markov Chain imbeddable variables of binomial type |
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443 | (3) |
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Waiting time distributions associated with MVB's |
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446 | (2) |
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The number of runs and patterns as members of the MVB family |
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448 | (6) |
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Multivariate MVB distributions |
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454 | (3) |
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Multivariate success runs distributions |
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457 | (9) |
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Alternative methods for exact distribution evaluation |
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466 | (7) |
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470 | (3) |
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Modelling Image Analysis Problems Using Markov Random Fields |
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473 | (42) |
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473 | (2) |
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475 | (5) |
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Markov random fields and Gibbs distributions |
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480 | (9) |
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489 | (10) |
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499 | (16) |
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507 | (1) |
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507 | (8) |
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An Introduction to Semi-Markov Processes with Application to Reliability |
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515 | (42) |
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515 | (1) |
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516 | (2) |
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Markov renewal processes (MRP) |
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518 | (7) |
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Semi-Markov processes with an arbitrary state space |
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525 | (3) |
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528 | (4) |
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532 | (5) |
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537 | (3) |
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540 | (2) |
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Some recent approaches to semi-Markov processes |
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542 | (9) |
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Reliability modeling and estimation |
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551 | (6) |
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554 | (3) |
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Departures and Related Characteristics in Queueing Models |
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557 | (16) |
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557 | (1) |
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Characterization/identifiability via output processes |
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558 | (6) |
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Characterization/identifiability via infinite divisibility property |
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564 | (4) |
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Strong unimodality and other relevant properties |
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568 | (5) |
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570 | (3) |
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Discrete Variate Time Series |
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573 | (34) |
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573 | (2) |
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575 | (1) |
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576 | (2) |
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578 | (16) |
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594 | (3) |
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State space and Bayesian models |
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597 | (5) |
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602 | (5) |
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602 | (5) |
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Extreme Value Theory, Models and Simulation |
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607 | (86) |
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607 | (1) |
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Limit laws in univariate extremes and characterizations |
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608 | (5) |
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613 | (5) |
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Generalized extreme value (GEV) distribution |
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618 | (2) |
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Generalized Pareto (GP) distribution |
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620 | (3) |
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Joint distribution of the r-largest order statistics |
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623 | (1) |
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A point process characterization |
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624 | (1) |
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Extremes of stochastic processes |
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625 | (10) |
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Limit laws for multivariate extremes |
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635 | (2) |
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Characterizations of the domain of attraction |
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637 | (12) |
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Characterizations of multivariate extreme value distributions |
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649 | (3) |
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652 | (2) |
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Parametric families for bivariate extreme value distributions |
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654 | (9) |
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Parametric families for multivariate extreme value distributions |
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663 | (14) |
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Extremes of multivariate stochastic processes |
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677 | (16) |
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679 | (1) |
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680 | (13) |
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Biological Applications of Branching Processes |
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693 | (82) |
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693 | (2) |
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History, surnames, and sex |
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695 | (8) |
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703 | (25) |
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728 | (10) |
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Ecology and conservation modelling |
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738 | (37) |
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762 | (13) |
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Markov Chain Approaches to Damage Models |
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775 | (20) |
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775 | (1) |
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Modified versions of some basic results on damage models |
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776 | (6) |
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Characterizations based on modified Rao--Rubin conditions |
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782 | (6) |
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Characterization via conditional expectations |
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788 | (7) |
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793 | (2) |
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Point Processes in Astronomy: Exciting Events in the Universe |
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795 | (32) |
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Introduction: what's the point? |
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795 | (2) |
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Unique features of astronomical point processes |
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797 | (1) |
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Naive point process theory |
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798 | (3) |
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The mystery of Gamma Ray bursts |
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801 | (14) |
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Other examples of astronomical point processes |
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815 | (7) |
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822 | (5) |
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823 | (1) |
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823 | (4) |
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On the Theory of Discrete and Continuous Bilinear Time Series Models |
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827 | (44) |
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827 | (6) |
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Linear time series models and cumulant spectra |
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833 | (1) |
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Volterra expansion and bilinear models |
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834 | (3) |
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Higher-order moments and identification |
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837 | (1) |
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Estimation of higher-order cumulants and the bilinear models |
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838 | (5) |
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Multivariate nonlinear time series and higher-order cumulants of random vectors |
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843 | (4) |
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Spurious regression and cointegration, nonlinearity |
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847 | (3) |
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Time dependent nonlinear models |
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850 | (2) |
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852 | (9) |
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Stationary bilinear process in continuous time |
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861 | (10) |
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866 | (1) |
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867 | (4) |
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Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study |
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871 | (60) |
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871 | (3) |
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874 | (13) |
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Nonlinear and non-Gaussian state-space modeling |
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887 | (19) |
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906 | (11) |
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Summary and concluding remarks |
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917 | (9) |
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Appendix A. Linear and normal system |
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919 | (1) |
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Appendix B. Sampling methods |
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920 | (3) |
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Appendix C. Recursive versus non-recursive algorithms |
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923 | (3) |
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926 | (1) |
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926 | (5) |
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Markov Modelling of Burst Behaviour in Ion Channels |
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931 | (38) |
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931 | (3) |
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934 | (5) |
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939 | (6) |
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945 | (4) |
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A five-state ligand-activated ion channel model |
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949 | (2) |
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A linear sequential model with drug blockade |
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951 | (4) |
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A model showing biphasic drug effects |
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955 | (3) |
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A model for a supergated double-barrelled chloride channel |
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958 | (5) |
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Some comments on statistical inference |
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963 | (6) |
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964 | (1) |
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965 | (1) |
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965 | (4) |
| Subject Index |
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969 | (10) |
| Contents of Previous Volumes |
|
979 | |
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