An Introduction to the Theory of Point Processes - Softcover

Inhaltsangabe

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.

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