Stochastic geometry: lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer [u.a.]
2007
|
| Series: | Lecture notes in mathematics
1892 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 284 S. |
| ISBN: | 3540381740 9783540381747 |
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MARC
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| 245 | 1 | 0 | |a Stochastic geometry |b lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 |c A. Baddeley ... Ed. W. Weil |
| 264 | 1 | |a Berlin [u.a.] |b Springer [u.a.] |c 2007 | |
| 300 | |a XII, 284 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1892 | |
| 650 | 4 | |a Géométrie stochastique | |
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Record in the Search Index
| _version_ | 1804135717911134208 |
|---|---|
| adam_text | Contents
Spatial
Point
Processes
and their Applications
Adrian Baddeley
................................................. 1
1
Point Processes
............................................... 2
1.1
Point Processes in ID and 2D
............................... 2
1.2
Formulation of Point Processes
.............................. 3
1.3
Example: Binomial Process
................................. 6
1.4
Foundations
.............................................. 7
1.5
Poisson
Processes
......................................... 8
1.6
Distributional Characterisation
............................. 12
1.7
Transforming a Point Process
............................... 16
1.8
Marked Point Processes
.................................... 19
1.9
Distances in Point Processes
................................ 21
1.10
Estimation from Data
...................................... 23
1.11
Computer Exercises
....................................... 24
2
Moments and Summary Statistics
............................... 26
2.1
Intensity
................................................. 26
2.2
Intensity for Marked Point Processes
......................... 30
2.3
Second Moment Measures
.................................. 32
2.4
Second Moments for Stationary Processes
.................... 35
2.5
The X-function
........................................... 38
2.6
Estimation from Data
...................................... 39
2.7
Exercises
................................................. 40
3
Conditioning
.................................................. 42
3.1
Motivation
............................................... 42
3.2
Palm Distribution
......................................... 44
3.3
Palm Distribution for Stationary Processes
................... 49
3.4
Nearest Neighbour Function
................................ 51
3.5
Conditional Intensity
...................................... 52
3.6
J-function
................................................ 55
3.7
Exercises
................................................. 56
4
Modelling and Statistical Inference
.............................. 57
X
Contents
4.1 Motivation............................................... 57
4.2
Parametric
Modelling and Inference
......................... 58
4.3
Finite Point Processes
..................................... 61
4.4
Point Process Densities
.................................... 62
4.5
Conditional Intensity
...................................... 64
4.6
Finite Gibbs Models
....................................... 66
4.7
Parameter Estimation
..................................... 69
4.8
Estimating Equations
...................................... 70
4.9
Likelihood Devices
........................................ 72
References
...................................................... 73
Random Polytopes, Convex Bodies, and Approximation
Imre Bárány....................................................
77
1
Introduction
.................................................. 77
2
Computing
Έφ(Κη)
............................................ 79
3
Minimal Caps and a General Result
............................. 80
4
The Volume of the Wet Part
.................................... 82
5
The Economic Cap Covering Theorem
........................... 84
6
Macbeath Regions
............................................. 84
7
Proofs of the Properties of the M-regions
......................... 87
8
Proof of the Cap Covering Theorem
............................. 89
9
Auxiliary Lemmas from Probability
.............................. 92
10
Proof of Theorem
3.1.......................................... 95
11
Proof of Theorem
4.1.......................................... 96
12
Proof of
(4)................................................... 98
13
Expectation of fk(Kn)
.........................................101
14
Proof of Lemma
13.2 ..........................................102
15
Further Results
...............................................104
16
Lattice Polytopes
..............................................108
17
Approximation
................................................109
18
How It All Began: Segments on the Surface of AT
..................114
References
......................................................115
Integral Geometric Tools for Stochastic Geometry
Rolf Schneider
...................................................119
Introduction
.....................................................119
1
From Hitting Probabilities to Kinematic Formulae
.................120
1.1
A Heuristic Question on Hitting Probabilities
.................120
1.2 Steiner
Formula and Intrinsic Volumes
.......................123
1.3
Hadwiger s Characterization Theorem for Intrinsic Volumes
.....126
1.4
Integral Geometric Formulae
................................129
2
Localizations and Extensions
....................................136
2.1
The Kinematic Formula for Curvature Measures
...............136
2.2
Additive Extension to Polyconvex Sets
.......................143
2.3
Curvature Measures for More General Sets
...................148
Contents
XI
3
Translative
Integral
Geometry
..................................151
3.1
The Principal
Translative Formula
for Curvature Measures
.....152
3.2
Basic Mixed Functionals and Support Functions
...............157
3.3
Further Topics of
Translative
Integral Geometry
...............163
4
Measures on Spaces of Flats
....................................164
4.1
Minkowski Spaces
.........................................165
4.2
Projective
Finsler Spaces
...................................173
4.3
Nonstationary
Hyperplane
Processes
.........................177
References
......................................................181
Random Sets (in Particular Boolean Models)
Wolfgang Weil
...................................................185
Introduction
.....................................................185
1
Random Sets, Particle Processes and Boolean Models
..............186
1.1
Random Closed Sets
.......................................187
1.2
Particle Processes
.........................................190
1.3
Boolean Models
...........................................194
2
Mean Values of Additive Functionals
.............................198
2.1
A General Formula for Boolean Models
......................199
2.2
Mean Values for RACS
....................................204
2.3
Mean Values for Particle Processes
..........................208
2.4
Quermass Densities of Boolean Models
.......................210
2.5
Ergodicity
................................................214
3
Directional Data, Local Densities, Nonstationary Boolean Models
.... 214
3.1
Directional Data and Associated Bodies
......................215
3.2
Local Densities
............................................222
3.3
Nonstationary Boolean Models
..............................224
3.4
Sections of Boolean Models
.................................230
4
Contact Distributions
..........................................231
4.1
Contact Distribution with Structuring Element
...............232
4.2
Generalized Contact Distributions
...........................237
4.3
Characterization of Convex Grains
..........................241
References
......................................................243
Random Mosaics
Daniel Hug
......................................................247
1
General Results
...............................................247
1.1
Basic Notions
.............................................247
1.2
Random Mosaics
..........................................248
1.3
Face-Stars
................................................250
1.4
Typical Cell and Zero Cell
..................................252
2
Voronoi and Delaunay Mosaics
..................................253
2.1
Voronoi Mosaics
...........................................253
2.2
Delaunay Mosaics
.........................................255
3 Hyperplane
Mosaics
...........................................257
XII Contents
4
Kendall s Conjecture
...........................................260
4.1
Large Cells in
Poisson
Hyperplane
Mosaics
...................261
4.2
Large Cells in
Poisson-
Voronoi Mosaics
......................263
4.3
Large Cells in Poisson-Delaunay Mosaics
.....................264
References
......................................................265
On the Evolution Equations of Mean Geometric Densities
for a Class of Space and Time Inhomogeneous Stochastic
Birth-and-growth Processes
Vincenzo Capasso,
Elena Villa
.....................................267
1
Introduction
..................................................267
2
Birth-and-growth Processes
.....................................268
2.1
The Nucleation Process
....................................268
2.2
The Growth Process
.......................................270
3
Closed Sets as Distributions
....................................271
3.1
The Deterministic Case
....................................271
3.2
The Stochastic Case
.......................................273
4
The Evolution Equation of Mean Densities for the Stochastic
Birth-and-growth Process
......................................274
4.1
Hazard Function and Causal Cone
...........................276
References
......................................................280
|
| adam_txt |
Contents
Spatial
Point
Processes
and their Applications
Adrian Baddeley
. 1
1
Point Processes
. 2
1.1
Point Processes in ID and 2D
. 2
1.2
Formulation of Point Processes
. 3
1.3
Example: Binomial Process
. 6
1.4
Foundations
. 7
1.5
Poisson
Processes
. 8
1.6
Distributional Characterisation
. 12
1.7
Transforming a Point Process
. 16
1.8
Marked Point Processes
. 19
1.9
Distances in Point Processes
. 21
1.10
Estimation from Data
. 23
1.11
Computer Exercises
. 24
2
Moments and Summary Statistics
. 26
2.1
Intensity
. 26
2.2
Intensity for Marked Point Processes
. 30
2.3
Second Moment Measures
. 32
2.4
Second Moments for Stationary Processes
. 35
2.5
The X-function
. 38
2.6
Estimation from Data
. 39
2.7
Exercises
. 40
3
Conditioning
. 42
3.1
Motivation
. 42
3.2
Palm Distribution
. 44
3.3
Palm Distribution for Stationary Processes
. 49
3.4
Nearest Neighbour Function
. 51
3.5
Conditional Intensity
. 52
3.6
J-function
. 55
3.7
Exercises
. 56
4
Modelling and Statistical Inference
. 57
X
Contents
4.1 Motivation. 57
4.2
Parametric
Modelling and Inference
. 58
4.3
Finite Point Processes
. 61
4.4
Point Process Densities
. 62
4.5
Conditional Intensity
. 64
4.6
Finite Gibbs Models
. 66
4.7
Parameter Estimation
. 69
4.8
Estimating Equations
. 70
4.9
Likelihood Devices
. 72
References
. 73
Random Polytopes, Convex Bodies, and Approximation
Imre Bárány.
77
1
Introduction
. 77
2
Computing
Έφ(Κη)
. 79
3
Minimal Caps and a General Result
. 80
4
The Volume of the Wet Part
. 82
5
The Economic Cap Covering Theorem
. 84
6
Macbeath Regions
. 84
7
Proofs of the Properties of the M-regions
. 87
8
Proof of the Cap Covering Theorem
. 89
9
Auxiliary Lemmas from Probability
. 92
10
Proof of Theorem
3.1. 95
11
Proof of Theorem
4.1. 96
12
Proof of
(4). 98
13
Expectation of fk(Kn)
.101
14
Proof of Lemma
13.2 .102
15
Further Results
.104
16
Lattice Polytopes
.108
17
Approximation
.109
18
How It All Began: Segments on the Surface of AT
.114
References
.115
Integral Geometric Tools for Stochastic Geometry
Rolf Schneider
.119
Introduction
.119
1
From Hitting Probabilities to Kinematic Formulae
.120
1.1
A Heuristic Question on Hitting Probabilities
.120
1.2 Steiner
Formula and Intrinsic Volumes
.123
1.3
Hadwiger's Characterization Theorem for Intrinsic Volumes
.126
1.4
Integral Geometric Formulae
.129
2
Localizations and Extensions
.136
2.1
The Kinematic Formula for Curvature Measures
.136
2.2
Additive Extension to Polyconvex Sets
.143
2.3
Curvature Measures for More General Sets
.148
Contents
XI
3
Translative
Integral
Geometry
.151
3.1
The Principal
Translative Formula
for Curvature Measures
.152
3.2
Basic Mixed Functionals and Support Functions
.157
3.3
Further Topics of
Translative
Integral Geometry
.163
4
Measures on Spaces of Flats
.164
4.1
Minkowski Spaces
.165
4.2
Projective
Finsler Spaces
.173
4.3
Nonstationary
Hyperplane
Processes
.177
References
.181
Random Sets (in Particular Boolean Models)
Wolfgang Weil
.185
Introduction
.185
1
Random Sets, Particle Processes and Boolean Models
.186
1.1
Random Closed Sets
.187
1.2
Particle Processes
.190
1.3
Boolean Models
.194
2
Mean Values of Additive Functionals
.198
2.1
A General Formula for Boolean Models
.199
2.2
Mean Values for RACS
.204
2.3
Mean Values for Particle Processes
.208
2.4
Quermass Densities of Boolean Models
.210
2.5
Ergodicity
.214
3
Directional Data, Local Densities, Nonstationary Boolean Models
. 214
3.1
Directional Data and Associated Bodies
.215
3.2
Local Densities
.222
3.3
Nonstationary Boolean Models
.224
3.4
Sections of Boolean Models
.230
4
Contact Distributions
.231
4.1
Contact Distribution with Structuring Element
.232
4.2
Generalized Contact Distributions
.237
4.3
Characterization of Convex Grains
.241
References
.243
Random Mosaics
Daniel Hug
.247
1
General Results
.247
1.1
Basic Notions
.247
1.2
Random Mosaics
.248
1.3
Face-Stars
.250
1.4
Typical Cell and Zero Cell
.252
2
Voronoi and Delaunay Mosaics
.253
2.1
Voronoi Mosaics
.253
2.2
Delaunay Mosaics
.255
3 Hyperplane
Mosaics
.257
XII Contents
4
Kendall's Conjecture
.260
4.1
Large Cells in
Poisson
Hyperplane
Mosaics
.261
4.2
Large Cells in
Poisson-
Voronoi Mosaics
.263
4.3
Large Cells in Poisson-Delaunay Mosaics
.264
References
.265
On the Evolution Equations of Mean Geometric Densities
for a Class of Space and Time Inhomogeneous Stochastic
Birth-and-growth Processes
Vincenzo Capasso,
Elena Villa
.267
1
Introduction
.267
2
Birth-and-growth Processes
.268
2.1
The Nucleation Process
.268
2.2
The Growth Process
.270
3
Closed Sets as Distributions
.271
3.1
The Deterministic Case
.271
3.2
The Stochastic Case
.273
4
The Evolution Equation of Mean Densities for the Stochastic
Birth-and-growth Process
.274
4.1
Hazard Function and Causal Cone
.276
References
.280 |
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| genre | (DE-588)1071861417 Konferenzschrift 2004 Martina Franca gnd-content |
| genre_facet | Konferenzschrift 2004 Martina Franca |
| id | DE-604.BV021801942 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:48:11Z |
| indexdate | 2024-07-09T20:44:57Z |
| institution | BVB |
| isbn | 3540381740 9783540381747 |
| language | English |
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| physical | XII, 284 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer [u.a.] |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 A. Baddeley ... Ed. W. Weil Berlin [u.a.] Springer [u.a.] 2007 XII, 284 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1892 Géométrie stochastique Stochastische meetkunde gtt Stochastic geometry Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2004 Martina Franca gnd-content Stochastische Geometrie (DE-588)4133202-7 s DE-604 Baddeley, Adrian Sonstige oth Weil, Wolfgang 1945-2018 Sonstige (DE-588)1015070035 oth Lecture notes in mathematics 1892 (DE-604)BV000676446 1892 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015014436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 Lecture notes in mathematics Géométrie stochastique Stochastische meetkunde gtt Stochastic geometry Stochastische Geometrie (DE-588)4133202-7 gnd |
| subject_GND | (DE-588)4133202-7 (DE-588)1071861417 |
| title | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 |
| title_auth | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 |
| title_exact_search | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 |
| title_exact_search_txtP | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 |
| title_full | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 A. Baddeley ... Ed. W. Weil |
| title_fullStr | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 A. Baddeley ... Ed. W. Weil |
| title_full_unstemmed | Stochastic geometry lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 A. Baddeley ... Ed. W. Weil |
| title_short | Stochastic geometry |
| title_sort | stochastic geometry lectures given at the cime summer school held in martina franca italy september 13 18 2004 |
| title_sub | lectures given at the CIME Summer School held in Martina Franca, Italy, September 13 - 18, 2004 |
| topic | Géométrie stochastique Stochastische meetkunde gtt Stochastic geometry Stochastische Geometrie (DE-588)4133202-7 gnd |
| topic_facet | Géométrie stochastique Stochastische meetkunde Stochastic geometry Stochastische Geometrie Konferenzschrift 2004 Martina Franca |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015014436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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