New perspectives in stochastic geometry:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 585 S. Ill., graph. Darst. |
| ISBN: | 9780199232574 |
Internformat
MARC
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| 245 | 1 | 0 | |a New perspectives in stochastic geometry |c ed. by. Wilfrid S. Kendall ... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XX, 585 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 700 | 1 | |a Kendall, Wilfrid S. |e Sonstige |4 oth | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018646006 | ||
Datensatz im Suchindex
| _version_ | 1804140725025112064 |
|---|---|
| adam_text | CONTENTS
List of Contributors
xix
1
Classical stochastic geometry (Rolf Schneider
and Wolfgang Weil)
1
1.1
From geometric probabilities to stochastic geometry
-
a look
at the origins
1
1.2
Geometric tools
6
1.3
Point processes
14
1.4
Random sets
26
1.5
Geometric processes
30
1.6
Mean values of geometric functional
35
References
41
I NEW DEVELOPMENTS IN CLASSICAL
STOCHASTIC GEOMETRY
2
Random polytopes (Matthias Reitzner)
45
2.1
Introduction
45
2.2
Convex hull of uniform random points
47
2.2.1
Inequalities
47
2.2.2
Expectations
48
2.2.3
The floating body
50
2.2.4
Higher moments
54
2.2.5
Limit theorems
57
2.2.6
Large deviation inequalities
60
2.2.7
Convex hull peeling
64
2.3
Gaussian polytopes
65
2.3.1
Projections of high-dimensional simplices
66
2.4
Random points on convex surfaces
67
2.5
Convex hull of 0-1-polytopes
68
2.6
Intersection of halfspaces
69
2.6.1
Random polyhedra containing a convex set
69
2.6.2
The zero-cell
71
References
71
3
Modern random measures: Palm theory and
related models
( Günter Last) 77
3.1
Outline
77
3.2
Stationary random measures
79
3.3
Stationary marked random measures
85
3.4
Invariant transport-kernels
87
xii
Contents
3.5
Invariance
properties of Palm measures
90
3.6
Existence of balancing weighted transport-kernels
93
3.7
Mecke s characterization of Palm measures
94
3.8
Mass-stationarity
96
3.9
Stationary partitions
99
3.10
Matchings and point stationarity
103
References
108
4
Limit theorems in stochastic geometry
(
Tomasz
Schreiber)
111
4.1
Introduction
Ш
4.2
Theory of stabilization
112
4.2.1
Point-value stabilization
113
4.2.2
Add-one cost stabilization
114
4.2.3
Localization
115
4.2.4
Laws of large numbers
115
4.2.5
Convergence of variance
118
4.2.6
Central limit theorem
120
4.2.7
Binomial input and de-Poissonization
122
4.2.8
Moderate and large deviations
123
4.3
Some applications of stabilization theory
125
4.4
Nearly additive Euclidean functionals
128
4.4.1
Euclidean functionals
128
4.4.2
Laws of large numbers
129
4.4.3
Concentration inequalities and large deviations
131
4.5
Examples of nearly additive Euclidean functionals
132
4.6
Limit theory for germ-grain models
133
4.6.1
Results for stationary
Poisson
germ-grain process
134
4.6.2
Results for general germ-grain models
136
4.7
Clan-of-ancestors graphical construction
136
4.8
Further limit theory
139
References
140
5
Tessellations (Pierre Calka)
145
5.1
Definitions and basic properties of random tessellations
145
5.1.1
Introduction
145
5.1.2
Zero-cell, ergodic means and typical cell
147
5.2
Exact distributional results
150
5.2.1
Number of hyperfaces and distribution of the cell
conditioned on the number of hyperfaces
150
5.2.2
Typical fc-face of a section of
a Poisson-
Voronoi
tessellation
152
5.2.3
The circumscribed radius
154
5.3
Asymptotic results
155
5.3.1
D. G. Kendall s conjecture
155
5.3.2
Cells with a large inradius
159
Contents xiii
5.4
Iterated tessellations
160
5.4.1
Tessellations stable with respect to iteration
160
5.4.2
Iterated tessellations in telecommunications
163
References
164
II STOCHASTIC GEOMETRY AND
MODERN PROBABILITY
6
Percolation and random graphs (Remco van
der Hofstad) 173
6.1
Introduction and notation
173
6.2
Percolation
174
6.2.1
Critical behaviour
179
6.2.2
Percolation on the regular tree
183
6.2.3
Percolation on Td
188
6.2.4
Percolation in two dimensions
194
6.2.5
Percolation in high dimensions
203
6.2.6
Oriented percolation
206
6.2.7
Percolation on non-amenable graphs
208
6.2.8
Continuum percolation
211
6.3
Random graphs
213
6.3.1
Motivation
213
6.3.2
Models without geometry
217
6.3.3
Phase transition in models without geometry
226
6.3.4
Distances in models without geometry
227
6.3.5
Models with geometry
231
References
237
7
Random directed and on-line networks (Mathew D. Penrose
and Andrew R. Wade)
248
7.1
Introduction and definitions
248
7.2
Motivation and related models
252
7.3
Bhatt and Roy s MDST and Dickman-type distributions
253
7.3.1
Record values and rooted vertices in the MDST
253
7.3.2
Dickman limits
254
7.3.3
Dickman process
258
7.4
Total length, stabilization, and phase transitions
261
7.4.1
The directed linear tree
261
7.4.2
Bhatt and Roy s south-west MDST
262
7.4.3
The on-line nearest-neighbour graph
263
7.4.4
The south MDST
264
7.5
The radial spanning tree
265
7.6
Future directions and open problems
266
7.6.1
More general point sets
266
7.6.2
CLT for the length of the planar ONG
267
7.6.3
CLT for total length of the RST
267
xiv Contents
7.6.4
Convergence
of measures
268
7.6.5
Degree distributions
269
7.6.6
Diameter and radius
270
7.6.7
Path convergence
270
7.6.8
Tessellations
270
References
271
8
Random fractals (Peter
Mörters)
275
8.1
Introduction
275
8.2
Representing fractals by trees
277
8.2.1
Fractals and trees
277
8.2.2
Galton-Watson fractals
279
8.2.3
The dimension of the zero-set of Brownian motion
283
8.3
Fine properties of stochastic processes
285
8.3.1
Favourite points of planar Brownian motion
286
8.3.2
The multifractal spectrum of intersection local time
290
8.3.3
Points of infinite multiplicity
295
8.4
More on the planar Brownian path
297
8.4.1
The Mandelbrot conjecture
297
8.4.2
More on the geometry of the Brownian frontier
300
References
302
III STATISTICS AND STOCHASTIC GEOMETRY
9
Inference
(Jesper M0ller)
307
9.1
Spatial point processes and other random closed
set models
307
9.2
Outline and some notation
307
9.3
Inference for
Poisson
and Cox process models
308
9.3.1
Definition and fundamental properties of
Poisson
and Cox processes
308
9.3.2
Modelling intensity
310
9.3.3
Simulation
312
9.3.4
Maximum likelihood
313
9.3.5
Moments
314
9.3.6
Summary statistics and residuals
315
9.3.7
Composite likelihood and minimum contrast
estimation
318
9.3.8
Simulation-based Bayesian inference
319
9.4
Inference for Gibbs point processes
321
9.4.1
Gibbs point processes
323
9.4.2
Modelling conditional intensity
326
9.4.3
Residuals and summary statistics
328
9.4.4
Simulation-based maximum likelihood inference
329
9.4.5
Pseudo-likelihood
330
Contents xv
9.4.6
Simulation-based Bayesian inference
332
9.4.7 Simulation
algorithms
335
References
340
10
Statistical shape theory
(
Wilfrid S. Kendall and Huiling
Le)
348
10.1
Motivations
348
10.2
Concepts
352
10.3
Geometry of shape
354
10.4
Distributions of shape
359
10.5
Some topics in shape statistics
361
10.5.1
Mean shapes and regression
361
10.5.2
MCMC techniques
366
10.6
Two recent applications
367
10.6.1
Random
Betti
numbers
367
10.6.2
Radon shape diffusion
368
References
370
11
Set estimation
{Antonio Cuevas
and
Ricardo
Fraiman)
374
11.1
Introduction
374
11.2
The problems under study
375
11.2.1
Support estimation
375
11.2.2
Boundary estimation
379
11.2.3
Level set estimation
381
11.2.4
Estimation in problems with covariates
384
11.2.5
Estimation of functionals and hypothesis testing
problems related to the support
386
11.3
On optimal convergence rates
387
11.4
Some mathematical tools
388
11.5
Further applications
392
References
393
12
Data depth: multivariate statistics and geometry
[Ignacio Cascos)
398
12.1
Introduction, background and history of data depth
398
12.2
Notions of data depth
401
12.2.1 Halfspace
depth
402
12.2.2
Simplicial depth
404
12.2.3
Zonoid depth
406
12.2.4
Other notions of data depth
408
12.3
Applications
411
12.3.1
Multivariate goodness-of-fit
411
12.3.2
Bagplot
411
12.3.3
Location estimates
412
12.3.4
Scatter estimates
413
12.3.5
Risk measurement
413
xv.
Contents
12.4
Algorithms
414
12.5
Stochastic orderings
415
12.5.1
Quantile orderings
415
12.5.2
Variability orderings
416
12.5.3
Stochastic orderings for random sets
418
12.6
Parameter depth and other concepts of depth
418
References
420
IV APPLICATIONS
13
Applications of stochastic geometry in image analysis
(Marie-Colette
N.M.
van
Lieshout)
427
13.1
Introduction
427
13.2
Stochastic geometric models: From random fields to
object processes
428
13.2.1
Random fields
428
13.2.2
Intermediate level modelling
431
13.2.3
Object processes
434
13.3
Properties and connections
437
13.3.1
Merging of labels
438
13.3.2
The length-weighted
Arak
field is a hard core
object process
439
13.4
Examples
440
13.4.1
Motion tracking
440
13.4.2
Foreground/background separation
442
References
445
14
Stereology
(
Werner
Nagel)
451
14.1
Motivation
451
14.2
From higher to lower dimension
-
sections and
induced mappings
452
14.3
A general integral equation
455
14.4
Some perspectives
456
14.4.1
The capacity functional
456
14.4.2
Intrinsic volumes and mixed functionals
-
the
application of integral geometry
458
14.4.3
Normal measures and orientation analysis
462
14.4.4
Size and shape distribution of particles
464
14.4.5
Arrangement of particles
-
second order
quantities
466
14.4.6
Tessellations
468
14.5
Properties that are inherited by section profiles
469
14.6
Uniqueness problems
471
14.7
Statistical aspects
472
References
474
Contents xvii
15
Physics of spatially structured materials (Klaus Mecke)
476
15.1
Introduction
476
15.2
Imaging of spatially structured materials: measuring
stochastic geometries
476
15.2.1
X-ray scattering: measuring correlation functions
478
15.2.2
Fluorescence confocal microscopy: spatial
information in real space
481
15.2.3
Scanning probe microscopy: two-dimensional
images
484
15.2.4
Computed tomography: three-dimensional images
487
15.3
Characterizing and modelling: utilizing intrinsic volumes
for image analysis
491
15.3.1
Characterizing thin films by Gaussian
random field
493
15.3.2
Modelling complex materials by Boolean models
497
15.4
Structure-property relations: physics based on
intrinsic volumes
501
15.4.1
Thermodynamic properties of confined fluids
502
15.4.2
Numerical test of additivity for a hard-sphere fluid
508
15.4.3
Transport properties and Boolean model
511
15.4.4
Outlook: elastic properties and tensor
valuations
512
References
513
16
Stochastic geometry and telecommunications networks
(Sergei Zuyev)
520
16.1
Crash course on telecommunications
520
16.1.1
Circuit switched telephony
521
16.1.2
Internet and P2P networks
522
16.1.3
Cellular telephony
523
16.1.4
Wireless ad hoc networks
526
16.1.5
Further reading
527
16.2
Stochastic geometry modelling
528
16.2.1
Fixed line networks: the last mile to go
529
16.2.2
Modelling cellular mobile networks
534
16.2.3
Modelling ad hoc networks
540
16.3
Conclusion
547
References
547
17
Random sets in finance and econometrics (liya Molchanov)
555
17.1
Introduction
555
17.2
Transaction costs
558
17.2.1
Cone models of transaction costs
558
17.2.2
Models with a money account
560
17.2.3
Existence of martingale selections
562
і
Contents
17.3
Risk measures
564
17.3.1
Coherent utility functions
564
17.3.2
Choquet integral and risk measures
566
17.3.3
Multivariate risk measures
568
17.4
Lift zonoids of asset prices
570
17.5
Partially identified models in econometrics
571
17.5.1
Linear models with interval response
571
17.5.2
Selection identification problems
572
References
573
Index
578
|
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| indexdate | 2024-07-09T22:04:32Z |
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| isbn | 9780199232574 |
| language | English |
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| spelling | New perspectives in stochastic geometry ed. by. Wilfrid S. Kendall ... 1. publ. Oxford [u.a.] Oxford Univ. Press 2010 XX, 585 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stochastic geometry Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 s DE-604 Kendall, Wilfrid S. Sonstige oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018646006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | New perspectives in stochastic geometry Stochastic geometry Stochastische Geometrie (DE-588)4133202-7 gnd |
| subject_GND | (DE-588)4133202-7 |
| title | New perspectives in stochastic geometry |
| title_auth | New perspectives in stochastic geometry |
| title_exact_search | New perspectives in stochastic geometry |
| title_full | New perspectives in stochastic geometry ed. by. Wilfrid S. Kendall ... |
| title_fullStr | New perspectives in stochastic geometry ed. by. Wilfrid S. Kendall ... |
| title_full_unstemmed | New perspectives in stochastic geometry ed. by. Wilfrid S. Kendall ... |
| title_short | New perspectives in stochastic geometry |
| title_sort | new perspectives in stochastic geometry |
| topic | Stochastic geometry Stochastische Geometrie (DE-588)4133202-7 gnd |
| topic_facet | Stochastic geometry Stochastische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018646006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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