Stochastic and integral geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Probability and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 693 S. 235 mm x 155 mm |
| ISBN: | 9783540788584 |
Internformat
MARC
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| 100 | 1 | |a Schneider, Rolf |d 1940- |e Verfasser |0 (DE-588)129512877 |4 aut | |
| 245 | 1 | 0 | |a Stochastic and integral geometry |c Rolf Schneider ; Wolfgang Weil |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XI, 693 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Probability and its applications | |
| 650 | 4 | |a Geometric probabilities | |
| 650 | 4 | |a Integral geometry | |
| 650 | 4 | |a Stochastic geometry | |
| 650 | 0 | 7 | |a Integralgeometrie |0 (DE-588)4161911-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Geometrie |0 (DE-588)4133202-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Geometrie |0 (DE-588)4133202-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Integralgeometrie |0 (DE-588)4161911-0 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Weil, Wolfgang |d 1945-2018 |e Verfasser |0 (DE-588)1015070035 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-78859-1 |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733456&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016733456 | ||
Datensatz im Suchindex
| _version_ | 1804138010976976896 |
|---|---|
| adam_text | Contents
1 Prolog..................................................... 1
1.1
Introduction
............................................ 1
1.2 General
Hints to the Literature
........................... 8
1.3
Notation and Conventions
................................ 10
Part I Foundations of Stochastic Geometry
2
Random Closed Sets
....................................... 17
2.1
Random Closed Sets in Locally Compact Spaces
............. 17
2.2
Characterization of Capacity
Funcţionale
................... 22
2.3
Some Consequences of
Choqueťs
Theorem
.................. 31
2.4
Random Closed Sets in Euclidean Space
.................... 37
3
Point Processes
............................................ 47
3.1
Random Measures and Point Processes
..................... 48
3.2
Poisson
Processes
........................................ 58
3.3
Palm Distributions
...................................... 70
3.4
Palm Distributions
-
General Approach
.................... 79
3.5
Marked Point Processes
.................................. 82
3.6
Point Processes of Closed Sets
............................ 95
4
Geometric Models
......................................... 99
4.1
Particle Processes
.......................................100
4.2
Germ-grain Processes
....................................109
4.3
Germ-grain Models. Boolean Models
.......................117
4.4
Processes of Flats
.......................................124
4.5
Surface Processes
........................................140
4.6
Associated Convex Bodies
................................145
Contents
Part II
Integral
Geometry
Averaging with Invariant Measures
........................167
5.1
The Kinematic Formula for Additive
Funcţionale
............168
5.2
Translative
Integral Formulas
.............................180
5.3
The Principal Kinematic Formula for Curvature Measures
.... 190
5.4
Intersection Formulas for Submanifolds
.....................203
Extended Concepts of Integral Geometry
..................211
6.1
Rotation Means of Minkowski Sums
.......................211
6.2
Projection Formulas
.....................................220
6.3
Cylinders and Thick Sections
.............................223
6.4
Translative
Integral Geometry, Continued
..................228
6.5
Spherical Integral Geometry
..............................248
Integral Geometric Transformations
.......................265
7.1
Flag Spaces
.............................................266
7.2
Blaschke-Petkantschin Formulas
...........................270
7.3
Transformation Formulas Involving Spheres
.................287
Part III Selected Topics from Stochastic Geometry
8
Some Geometric Probability Problems
.....................293
8.1
Historical Examples
.....................................293
8.2
Convex Hulls of Random Points
...........................298
8.3
Random Projections of Polytopes
..........................328
8.4
Randomly Moving Bodies and Flats
.......................335
8.5
Touching Probabilities
...................................349
8.6
Extremal Problems for Probabilities and Expectations
.......359
9
Mean Values for Random Sets
.............................377
9.1
Formulas for Boolean Models
.............................379
9.2
Densities of Additive Functionals
..........................393
9.3
Ergodic Densities
........................................404
9.4
Intersection Formulas and Unbiased Estimators
.............413
9.5
Further Estimation Problems
.............................429
10
Random. Mosaics
..........................................445
10.1
Mosaics as Particle Processes
.............................446
10.2
Voronoi and Delaunay Mosaics
............................470
10.3 Hyperplane
Mosaics
.....................................484
10.4
Zero Cells and Typical Cells
..............................493
10.5
Mixing Properties
.......................................515
Contents
XI
11
Non-stationary
Models ....................................521
11.1
Particle Processes and Boolean Models
.....................522
11.2
Contact Distributions
...................................534
11.3
Processes of Flats
.......................................543
11.4
Tessellations
............................................550
Part IV Appendix
12
Facts from General Topology
..............................559
12.1
General Topology and
Borei
Measures
......................559
12.2
The Space of Closed Sets
.................................563
12.3
Euclidean Spaces and Hausdorff Metric
.....................570
13
Invariant Measures
........................................575
13.1
Group Operations and Invariant Measures
..................575
13.2
Homogeneous Spaces of Euclidean Geometry
................581
13.3
A General Uniqueness Theorem
...........................593
14
Facts from Convex Geometry
..............................597
14.1
The Subspace Determinant
...............................597
14.2
Intrinsic Volumes and Curvature Measures
..................599
14.3
Mixed Volumes and Inequalities
...........................610
14.4
Additive Functional
.....................................617
14.5
Hausdorff Measures and Rectifiable Sets
....................633
References
.....................................................637
Author Index
..................................................675
Subject Index
.................................................681
Notation Index
................................................689
|
| adam_txt |
Contents
1 Prolog. 1
1.1
Introduction
. 1
1.2 General
Hints to the Literature
. 8
1.3
Notation and Conventions
. 10
Part I Foundations of Stochastic Geometry
2
Random Closed Sets
. 17
2.1
Random Closed Sets in Locally Compact Spaces
. 17
2.2
Characterization of Capacity
Funcţionale
. 22
2.3
Some Consequences of
Choqueťs
Theorem
. 31
2.4
Random Closed Sets in Euclidean Space
. 37
3
Point Processes
. 47
3.1
Random Measures and Point Processes
. 48
3.2
Poisson
Processes
. 58
3.3
Palm Distributions
. 70
3.4
Palm Distributions
-
General Approach
. 79
3.5
Marked Point Processes
. 82
3.6
Point Processes of Closed Sets
. 95
4
Geometric Models
. 99
4.1
Particle Processes
.100
4.2
Germ-grain Processes
.109
4.3
Germ-grain Models. Boolean Models
.117
4.4
Processes of Flats
.124
4.5
Surface Processes
.140
4.6
Associated Convex Bodies
.145
Contents
Part II
Integral
Geometry
Averaging with Invariant Measures
.167
5.1
The Kinematic Formula for Additive
Funcţionale
.168
5.2
Translative
Integral Formulas
.180
5.3
The Principal Kinematic Formula for Curvature Measures
. 190
5.4
Intersection Formulas for Submanifolds
.203
Extended Concepts of Integral Geometry
.211
6.1
Rotation Means of Minkowski Sums
.211
6.2
Projection Formulas
.220
6.3
Cylinders and Thick Sections
.223
6.4
Translative
Integral Geometry, Continued
.228
6.5
Spherical Integral Geometry
.248
Integral Geometric Transformations
.265
7.1
Flag Spaces
.266
7.2
Blaschke-Petkantschin Formulas
.270
7.3
Transformation Formulas Involving Spheres
.287
Part III Selected Topics from Stochastic Geometry
8
Some Geometric Probability Problems
.293
8.1
Historical Examples
.293
8.2
Convex Hulls of Random Points
.298
8.3
Random Projections of Polytopes
.328
8.4
Randomly Moving Bodies and Flats
.335
8.5
Touching Probabilities
.349
8.6
Extremal Problems for Probabilities and Expectations
.359
9
Mean Values for Random Sets
.377
9.1
Formulas for Boolean Models
.379
9.2
Densities of Additive Functionals
.393
9.3
Ergodic Densities
.404
9.4
Intersection Formulas and Unbiased Estimators
.413
9.5
Further Estimation Problems
.429
10
Random. Mosaics
.445
10.1
Mosaics as Particle Processes
.446
10.2
Voronoi and Delaunay Mosaics
.470
10.3 Hyperplane
Mosaics
.484
10.4
Zero Cells and Typical Cells
.493
10.5
Mixing Properties
.515
Contents
XI
11
Non-stationary
Models .521
11.1
Particle Processes and Boolean Models
.522
11.2
Contact Distributions
.534
11.3
Processes of Flats
.543
11.4
Tessellations
.550
Part IV Appendix
12
Facts from General Topology
.559
12.1
General Topology and
Borei
Measures
.559
12.2
The Space of Closed Sets
.563
12.3
Euclidean Spaces and Hausdorff Metric
.570
13
Invariant Measures
.575
13.1
Group Operations and Invariant Measures
.575
13.2
Homogeneous Spaces of Euclidean Geometry
.581
13.3
A General Uniqueness Theorem
.593
14
Facts from Convex Geometry
.597
14.1
The Subspace Determinant
.597
14.2
Intrinsic Volumes and Curvature Measures
.599
14.3
Mixed Volumes and Inequalities
.610
14.4
Additive Functional
.617
14.5
Hausdorff Measures and Rectifiable Sets
.633
References
.637
Author Index
.675
Subject Index
.681
Notation Index
.689 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV035064988 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:01:58Z |
| indexdate | 2024-07-09T21:21:24Z |
| institution | BVB |
| isbn | 9783540788584 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016733456 |
| oclc_num | 254625085 |
| open_access_boolean | |
| owner | DE-384 DE-29T DE-20 DE-19 DE-BY-UBM DE-703 DE-11 DE-898 DE-BY-UBR DE-739 DE-91G DE-BY-TUM DE-824 DE-83 DE-188 |
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| physical | XI, 693 S. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Probability and its applications |
| spelling | Schneider, Rolf 1940- Verfasser (DE-588)129512877 aut Stochastic and integral geometry Rolf Schneider ; Wolfgang Weil Berlin [u.a.] Springer 2008 XI, 693 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Probability and its applications Geometric probabilities Integral geometry Stochastic geometry Integralgeometrie (DE-588)4161911-0 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 s DE-604 Integralgeometrie (DE-588)4161911-0 s Weil, Wolfgang 1945-2018 Verfasser (DE-588)1015070035 aut Erscheint auch als Online-Ausgabe 978-3-540-78859-1 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733456&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schneider, Rolf 1940- Weil, Wolfgang 1945-2018 Stochastic and integral geometry Geometric probabilities Integral geometry Stochastic geometry Integralgeometrie (DE-588)4161911-0 gnd Stochastische Geometrie (DE-588)4133202-7 gnd |
| subject_GND | (DE-588)4161911-0 (DE-588)4133202-7 |
| title | Stochastic and integral geometry |
| title_auth | Stochastic and integral geometry |
| title_exact_search | Stochastic and integral geometry |
| title_exact_search_txtP | Stochastic and integral geometry |
| title_full | Stochastic and integral geometry Rolf Schneider ; Wolfgang Weil |
| title_fullStr | Stochastic and integral geometry Rolf Schneider ; Wolfgang Weil |
| title_full_unstemmed | Stochastic and integral geometry Rolf Schneider ; Wolfgang Weil |
| title_short | Stochastic and integral geometry |
| title_sort | stochastic and integral geometry |
| topic | Geometric probabilities Integral geometry Stochastic geometry Integralgeometrie (DE-588)4161911-0 gnd Stochastische Geometrie (DE-588)4133202-7 gnd |
| topic_facet | Geometric probabilities Integral geometry Stochastic geometry Integralgeometrie Stochastische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733456&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schneiderrolf stochasticandintegralgeometry AT weilwolfgang stochasticandintegralgeometry |