دانلود کتاب Point Process Calculus in Time and Space

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Preface Contents Chapter 1 Generalities 1.1 Point Processes as Random Measures 1.2 Campbell’s Formula and Moment Measures 1.3 The Distribution of a Point Process 1.4 Convergence in Distribution and Variation 1.5 Cluster Point Processes 1.6 The Stieltjes–Lebesgue Calculus 1.7 Exercises Chapter 2 Poisson Processes on the Line 2.1 Counting Process and Interval Sequence 2.2 The Smoothing Formula 2.3 Poisson Martingales and Stochastic Integrals 2.4 Watanabe’s Characterization 2.5 HMCs and Stochastic Differential Equations 2.6 HMCs and Time-Scaled HPPs 2.7 Exercises Chapter 3 Spatial Poisson Processes 3.1 Sampling a Poisson Process 3.2 The Covariance and Exponential Formulas 3.3 Marked Spatial Poisson Processes 3.4 Operations on Poisson Processes 3.5 Change of Probability 3.6 Exact Sampling of Cluster Point Processes 3.7 The Boolean Model 3.8 Exercises Chapter 4 Renewal and Regenerative Processes 4.1 Renewal Point processes 4.2 The Renewal Theorem 4.3 Blackwell’s Theorem and its Refinements 4.4 Regenerative Processes 4.5 Multivariate Renewal Equations 4.6 Semi-Markov Processes 4.7 Exercises Chapter 5 Point Processes with a Stochastic Intensity 5.1 The Smoothing Formulas 5.2 Regenerative Form of the Intensity Kernel 5.3 Martingales as Stochastic Integrals 5.4 Time Scaling 5.5 Continuous Change of Probability 5.6 Extension of the Theory of Stochastic Intensity 5.7 Grigelionis’ Representation 5.8 Origin and Motivation of the Martingale Approach 5.9 Exercises Chapter 6 Exvisible Intensity of Finite Point Processes 6.1 The Janossy Density 6.2 The Spatial Smoothing formula 6.3 Exvisibility and Predictability 6.4 Finite Markov Point Processes 6.5 Spatial Birth-and-Death Point Processes 6.6 An Alternative Model 6.7 Exercises Chapter 7 Palm Probability on the Line 7.1 Stationary Point Processes 7.2 A First Look at Palm Probability 7.3 Palm Theory on the Line: Basic Formulas 7.4 From Palm Probability to Stationary Probability 7.5 Local Interpretation of Palm Probability 7.6 The Cross-ergodic Theorem 7.7 Palm Probability and Stochastic Intensity 7.8 Exercises Chapter 8 Palm Probability in Space 8.1 The Voronoi Cell and the Inversion Formula 8.2 The Local Interpretation 8.3 Ergodicity 8.4 The Mecke Measure 8.5 The Reduced Mecke Measure 8.6 Exercises Chapter 9 The Power Spectral Measure 9.1 The Covariance Measure 9.2 The Bartlett Spectral Measure 9.3 Long-range Dependence 9.4 Transformations of the Spectral Measure 9.5 Exercises Chapter 10 The Information Content of Point Processes 10.1 Filtering 10.2 Separation of Detection and Filtering 10.3 Hiding Information in a Point Process 10.4 Noisy Points 10.5 Random Sampling 10.6 Exercises Chapter 11 Point Processes in Queueing 11.1 A Review of Markovian Queueing Theory 11.2 Poisson Systems 11.3 The G/G/1/∞ Queue 11.4 PASTA, Little, etc. 11.5 Selected Applications 11.6 Exercises Chapter 12 Hawkes Point Processes 12.1 As a Branching Point Process 12.2 Rates of Extinction and of Installation 12.3 The Bartlett Spectrum of the Hawkes Process 12.4 Exact Sampling of Hawkes Processes 12.5 Branching Point Processes Without Ancestor 12.6 Kerstan Point Processes 12.7 Exercises Appendix A.1 Measurability and Measure A.2 Stochastic Processes A.3 Martingales A.4 Internal History of a Marked Point Process A.5 Local vs. Global Absolute Continuity Bibliography Index