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An Introduction to the Theory of Point Processes Volume II: General Theory and Structure

:	D.J. Daley, David Vere-Jones
:	An Introduction to the Theory of Point Processes Volume II: General Theory and Structure
:	Springer-Verlag
:	9780387498355
:	2
:	CHF 142.50
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	573
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

	Preface to Volume II, Second Edition	7
	Contents	9
	Chapter Titles for Volume I	11
	Principal Notation	12
	Concordance of Statements from the First Edition	16
	9 Basic Theory of Random Measures and Point Processes	18
	9.1. Definitions and Examples	19
	9.2. Finite-Dimensional Distributions and the Existence Theorem	42
	9.3. Sample Path Properties: Atoms and Orderliness	55
	9.4. Functionals: Definitions and Basic Properties	69
	9.5. Moment Measures and Expansions of Functionals	82
	10 Special Classes of Processes	93
	10.1. Completely Random Measures	94
	10.2. In.nitely Divisible Point Processes	104
	10.3. Point Processes De.ned by Markov Chains	112
	10.4. Markov Point Processes	135
	11 Convergence Concepts and Limit Theorems	148
	11.1. Modes of Convergence for Random Measures and Point Processes	149
	11.2. Limit Theorems for Superpositions	163
	11.3. Thinned Point Processes	172
	11.4. Random Translations	183
	12 Stationary Point Processes and Random Measures	193
	12.1. Stationarity: Basic Concepts	194
	12.2. Ergodic Theorems	211
	12.3. Mixing Conditions	223
	12.4. Stationary In.nitely Divisible Point Processes	233
	12.5. Asymptotic Stationarity and Convergence to Equilibrium	239
	12.6. Moment Stationarity and Higher- order Ergodic Theorems	253
	12.7. Long-range Dependence	266
	12.8. Scale-invariance and Self-similarity	272
	13 Palm Theory	285
	13.1. Campbell Measures and Palm Distributions	286
	13.2. Palm Theory for Stationary Random Measures	301
	13.3. Interval- and Point-stationarity	316
	13.4. Marked Point Processes, Ergodic Theorems, and Convergence to Equilibrium	334
	13.5. Cluster Iterates	351
	13.6. Fractal Dimensions	357
	14 Evolutionary Processes and Predictability	372
	14.1. Compensators and Martingales	373
	14.2. Campbell Measure and Predictability	393
	14.3. Conditional Intensities	407
	14.4. Filters and Likelihood Ratios	417
	14.5. A Central Limit Theorem	429
	14.6. Random Time Change	435
	14.7. Poisson Embedding and Existence Theorems	443
	14.8. Point Process Entropy and a Shannon – MacMillan Theorem	457
	15 Spatial Point Processes	474
	15.1. Descriptive Aspects: Distance Properties	475
	15.2. Directional Properties and Isotropy	483
	15.3. Stationary Line Processes in the Plane	488
	15.4. Space–Time Processes	502
	15.5. The Papangelou Intensity and Finite Point Patterns	523
	15.6. Modi.ed Campbell Measures and Papangelou Kernels	535
	15.7. The Papangelou Intensity Measure and Exvisibility	543
	References with Index	554
	Subject Index	574