Verfügbarkeit: Stochastic and integral geometry | Technische Universität München

Stochastic and integral geometry:

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Bibliographische Detailangaben
Beteiligte Personen:	Schneider, Rolf 1940- (VerfasserIn), Weil, Wolfgang 1945-2018 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2008
Schriftenreihe:	Probability and its applications
Schlagwörter:	Geometric probabilities Integral geometry Stochastic geometry Integralgeometrie Stochastische Geometrie
Links:	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
Umfang:	XI, 693 S. 235 mm x 155 mm
ISBN:	9783540788584

Internformat

MARC


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245	1	0	\|a Stochastic and integral geometry \|c Rolf Schneider ; Wolfgang Weil
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300			\|a XI, 693 S. \|c 235 mm x 155 mm
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Datensatz im Suchindex

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DE-BY-TUM_katkey	1774982
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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
any_adam_object	1
author	Schneider, Rolf 1940- Weil, Wolfgang 1945-2018
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discipline	Mathematik Wirtschaftswissenschaften
format	Book
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isbn	9783540788584
language	English
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physical	XI, 693 S. 235 mm x 155 mm
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series2	Probability and its applications
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_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

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