An introduction to the theory of point processes: 1 Elementary theory and methods
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2005
|
| Edition: | 2. ed., 2. corr. print. |
| Series: | Probability and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 432 - 451 |
| Physical Description: | XXI, 469 S. |
| ISBN: | 0387955410 |
Staff View
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| 245 | 1 | 0 | |a An introduction to the theory of point processes |n 1 |p Elementary theory and methods |c D. J. Daley ; D. Vere-Jones |
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| 264 | 1 | |a New York [u.a.] |b Springer |c 2005 | |
| 300 | |a XXI, 469 S. | ||
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Record in the Search Index
| _version_ | 1804133579921293312 |
|---|---|
| adam_text | Titel: Bd. 1. An introduction to the theory of point processes. Elementary theory and methods
Autor: Daley, Daryl J.
Jahr: 2005
Contents
Preface to the Second Edition vii
Preface to the First Edition be
Principal Notation xvii
Concordance of Statements from the First Edition xxi
1 Early History 1
1.1 Life Tables and Renewal Theory 1
1.2 Counting Problems 8
1.3 Some More Recent Developments 13
2 Basic Properties of the Poisson Process 19
2.1 The Stationary Poisson Process 19
2.2 Characterizations of the Stationary Poisson Process:
I. Complete Randomness 26
2.3 Characterizations of the Stationary Poisson Process:
II. The Form of the Distribution 31
2.4 The General Poisson Process 34
3 Simple Results for Stationary Point Processes on the Line 41
3.1 Specification of a Point Process on the Line 41
3.2 Stationarity: Definitions 44
3.3 Mean Density, Intensity, and Batch-Size Distribution 46
3.4 Palm-Khinchin Equations 53
3.5 Ergodicity and an Elementary Renewal Theorem Analogue 60
3.6 Subadditive and Superadditive Functions 64
xiv Contents
4 Renewal Processes 66
4.1 Basic, Properties 66
4.2 Stationarity and Recurrence Times 74
4.3 Operations and Characterizations 78
4.4 Renewal Theorems 83
4.5 Neighbours of the Renewal Process: Wold Processes 92
4.6 Stieltjes-Integral Calculus and Hazard Measures 106
5 Finite Point Processes 111
5.1 An Elementary Example: Independently and Identically
Distributed Clusters 112
5.2 Factorial Moments, Cumulants, and Generating Function
Relations for Discrete Distributions 114
5.3 The General Finite Point Process: Definitions and Distributions 123
5.4 Moment Measures and Product Densities 132
5.5 Generating Functionals and Their Expansions 144
6 Models Constructed via Conditioning:
Cox, Cluster, and Marked Point Processes 157
6.1 Infinite Point Families and Random Measures 157
6.2 Cox (Doubly Stochastic Poisson) Processes 169
6.3 Cluster Processes 175
6.4 Marked Point Processes 194
7 Conditional Intensities and Likelihoods 211
7.1 Likelihoods and Janossy Densities 212
7.2 Conditional Intensities, Likelihoods, and Compensators 229
7.3 Conditional Intensities for Marked Point Processes 246
7.4 Random Time Change and a Goodness-of-Fit Test 257
7.5 Simulation and Prediction Algorithms 267
7.6 Information Gain and Probability Forecasts 275
8 Second-Order Properties of Stationary Point Processes 288
8.1 Second-Moment and Covariance Measures 289
8.2 The Bartlett Spectrum 303
8.3 Multivariate and Marked Point Processes 316
8.4 Spectral Representation 331
8.5 Linear Filters and Prediction 342
8.6 P.P.D. Measures 357
Contents xv
Al A Review of Some Basic Concepts of
Topology and Measure Theory 368
A 1.1 Set Theory 368
A1.2 Topologies 369
A1.3 Finitely and Countably Additive Set Functions 372
A 1.4 Aleasurable Functions and Integrals 374
A 1.5 Product Spaces 377
Al.6 Dissecting Systems and Atomic Measures 382
A2 Measures on Metric Spaces 384
A2.1 Borel Sets and the Support of Measures 384
A2.2 Regular and Tight Measures 386
A2.3 Weak Convergence of Measures 390
A2.4 Compactness Criteria for Weak Convergence 394
A2.5 Metric Properties of the Space Ì÷ 398
A2.6 Boundedly Finite Measures and the Space Ì÷ 402
A2.3 Measures on Topological Groups 407
A2.3 Fourier Transforms 411
A3 Conditional Expectations, Stopping Times,
and Martingales 414
A3.1 Conditional Expectations 414
A3.2 Convergence Concepts 418
A3.3 Processes and Stopping Times 423
A3.4 Martingales 428
References with Index 432
Subject Index 452
Chapter Titles for Volume II
9 General Theory of Point Processes and Random Measures
10 Special Classes of Processes
11 Convergence Concepts and Limit Theorems
12 Ergodic Theory and Stationary Processes
13 Palm Theory
14 Evolutionary Processes and Predictability
15 Spatial Point Processes
|
| any_adam_object | 1 |
| author | Daley, Daryl J. 1939- Vere-Jones, Daniel |
| author_GND | (DE-588)128971878 |
| author_facet | Daley, Daryl J. 1939- Vere-Jones, Daniel |
| author_role | aut aut |
| author_sort | Daley, Daryl J. 1939- |
| author_variant | d j d dj djd d v j dvj |
| building | Verbundindex |
| bvnumber | BV020019123 |
| ctrlnum | (OCoLC)225207361 (DE-599)BVBBV020019123 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., 2. corr. print. |
| format | Book |
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| id | DE-604.BV020019123 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:10:58Z |
| institution | BVB |
| isbn | 0387955410 |
| language | English |
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| physical | XXI, 469 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Probability and its applications |
| spelling | Daley, Daryl J. 1939- Verfasser (DE-588)128971878 aut An introduction to the theory of point processes 1 Elementary theory and methods D. J. Daley ; D. Vere-Jones 2. ed., 2. corr. print. New York [u.a.] Springer 2005 XXI, 469 S. txt rdacontent n rdamedia nc rdacarrier Probability and its applications Literaturverz. S. 432 - 451 Point processes Vere-Jones, Daniel Verfasser aut (DE-604)BV016503102 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013340521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Daley, Daryl J. 1939- Vere-Jones, Daniel An introduction to the theory of point processes Point processes |
| title | An introduction to the theory of point processes |
| title_auth | An introduction to the theory of point processes |
| title_exact_search | An introduction to the theory of point processes |
| title_full | An introduction to the theory of point processes 1 Elementary theory and methods D. J. Daley ; D. Vere-Jones |
| title_fullStr | An introduction to the theory of point processes 1 Elementary theory and methods D. J. Daley ; D. Vere-Jones |
| title_full_unstemmed | An introduction to the theory of point processes 1 Elementary theory and methods D. J. Daley ; D. Vere-Jones |
| title_short | An introduction to the theory of point processes |
| title_sort | an introduction to the theory of point processes elementary theory and methods |
| topic | Point processes |
| topic_facet | Point processes |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013340521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV016503102 |
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