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Point processes and queues: martingales dynamics

Author: Brémaud, Pierre Series: Springer series in statistics Publisher: Springer, 1981.Language: EnglishDescription: 354 p. : Ill. ; 24 cm.ISBN: 0387905367Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA274 .B74 1981
(Browse shelf)
001211964
Available 001211964
Total holds: 0

Includes bibliographical references and index

Digitized

Point Processes and Queues Martingale Dynamics Contents Acknowledgments Introduction Special Notations I Martingales 1. Histories and Stopping Times 2. Martingales 3. Predictability 4. Square-Integrable Martingales References Solutions to Exercises, Chapter I xi xiii xix 1 1 3 8 11 12 13 II Point Processes, Queues, and Intensities 1. Counting Processes and Queues 2. Watanabe's Characterization 3. Stochastic Intensity, General Case 4. Predictable Intensities 5. Representation of Queues 6. Random Changes of Time 7. Cryptographic Point Processes References Solutions to Exercises, Chapter II 18 18 23 27 30 35 40 43 47 48 III Integral Representation of Point-Process Martingales 1. The Structure of Internal Histories 2. Regenerative Form of the Intensity 3. The Representation Theorem 4. Hilbert-Space Theory of Poissonian Martingales 5. Useful Extensions References Solutions to Exercises, Chapter III 56 56 59 64 70 75 76 77 viii Contents IV Filtering I. The Theory of Innovations 2. State Estimates for Queues and Markov Chains 3. Continuous States and Nontrivial Prehistory References Solutions to Exercises, Chapter IV 83 83 100 107 115 115 V Flows in Markovian Networks of Queues 1. Single Station : The Historical Results and the Filtering Method 2. Jackson's Networks 3. Burke's Output Theorem for Networks 4. Cascades and Loops in Jackson's Networks 5. Independence and Poissonian Flows in Markov Chains References Solutions to Exercises, Chapter V 122 122 131 138 143 151 154 155 158 158 165 170 174 180 187 189 190 196 196 202 211 219 225 229 230 233 233 238 241 244 250 250 VI Likelihood Ratios 1. Radon-Nikodym Derivatives and Tests of Hypotheses 2. Changes of Intensities "a la Girsanov" 3. Filtering by the Method of the Probability of Reference 4. Applications 5. The Capacity of a Point-Process Channel 6. Detection Formula References Solutions to Exercises, Chapter VI VII Optimal Control 1. Modeling Intensity Controls 2. Dynamic Programming for Intensity Controls: Complete-Observation Case 3. Input Regulation. A Case Study in Impulsive Control 4. Attraction Controls 5. Existence via Likelihood Ratio References Solutions to Exercises, Chapter VII VIII Marked Point Processes 1. Counting Measure and Intensity Kernels 2. Martingale Representation and Filtering 3. Radon-Nikodym Derivatives 4. Towards a General Theory of Intensity References Solutions to Exercises, Chapter VIII Contents ix A 1 Background in Probability and Stochastic Processes 1. Introduction 2. Monotone Class Theorem 3. Random Variables 4. Expectations 5. Conditioning and Independence 6. Convergence 7. Stochastic Processes 8. Markov Processes References 255 255 256 261 266 275 285 287 290 295 A2 Stopping Times and Point -Process Histories 1. Stopping Times 2. Changes of Time and Meyer-Dellacherie's Integration Formula 3. Point-Process Histories References 296 296 300 303 311 A3 Wiener -Driven Dynamical Systems 1. Ito's Stochastic Integral 2. Square-Integrable Brownian Martingales 3. Girsanov's Theorem References 312 312 321 327 332 A4 Stieltjes -Lebesgue Calculus 1. The Stieltjes-Lebesgue Integral 2. The Product and Exponential Formulas References 334 334 336 339 General Bibliography Index 341 351

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