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AuthorDaley, D. J. author
TitleAn Introduction to the Theory of Point Processes [electronic resource] / by D. J. Daley, D. Vere-Jones
ImprintNew York, NY : Springer New York : Imprint: Springer, 1998
Connect tohttp://dx.doi.org/10.1007/978-1-4757-2001-3
Descript XXI, 702 p. 1 illus. online resource

SUMMARY

Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad historical perspective in an attempt to provide a wider audience with insights into recent theoretical developments. It contains numerous examples and exercises. This book aims to bridge the gap between informal treatments concerned with applications and highly abstract theoretical treatments


CONTENT

1 Early History -- 2 Basic Properties of the Poisson Process -- 3 Simple Results for Stationary Point Processes on the Line -- 4 Renewal Processes -- 5 Finite Point Processes -- 6 Introduction to the General Theory of Random Measures -- 7 Introduction to the General Theory of Point Processes -- 8 Cluster Processes, Infinitely Divisible Processes, and Doubly Stochastic Processes -- 9 Convergence Concepts and Limit Theorems -- 10 Stationary Point Processes and Random Measures -- 11 Spectral Theory -- 12 Palm Theory -- 13 Conditional Intensities and Likelihoods -- 14 Exterior Conditioning -- Appendix 1 A Review of Some Basic Concepts of Topology and Measure Theory -- A1.1. Set Theory -- A1.2. Topologies -- A1.3. Finitely and Countably Additive Set Functions -- A1.4. Measurable Functions and Integrals -- A1.5. Product Spaces -- Appendix 2 Measures on Metric Spaces -- A2.1. Borel Sets, Dissecting Systems, and Atomic and Diffuse Measures -- A2.2. Regular and Tight Measures -- A2.3. Weak Convergence of Measures -- A2.4. Compactness Criteria for Weak Convergence -- A2.7. Measures on Topological Groups -- A2.8. Fourier Transforms -- Appendix 3 Conditional Expectations, Stopping Times, and Martingales -- A3.1. Conditional Expectations -- A3.2. Convergence Concepts -- A3.3. Processes and Stopping Times -- A3.4. Martingales -- References and Author Index


Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes



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