Format:
Online-Ressource
Edition:
Third edition Sung Nok Chiu, Dietrich Stoyan, Wilfrid S. Kendall, Joseph Mecke
Edition:
Online-Ausg. Electronic reproduction; Available via World Wide Web
ISBN:
9781118658239
,
9781118658246
,
9781118658253
,
0470664819
,
1299940846
,
111865823X
,
9780470664810
,
9781299940840
,
9781118658239
Series Statement:
Wiley series in probability and statistics
Content:
"The previous edition of this book has served as the key reference in its field for over 20 years and is regarded as the best treatment of the subject of stochastic geometry. Extensively updated, this mew edition includes new sections on analytical and numerically tractable results and applications of Voronoi tessellations; introduces models such as Laguerre and iterated tessellations; and presents theoretical results. Statistics for planar point processes are introduced, and the text also includes a new section on random geometrical graphs and random networks"--
Content:
"Includes new sections such as random geometrical graphs and random networks and tractable results and applications of Voronoi tessellations"--
Content:
"The previous edition of this book has served as the key reference in its field for over 20 years and is regarded as the best treatment of the subject of stochastic geometry. Extensively updated, this mew edition includes new sections on analytical and numerically tractable results and applications of Voronoi tessellations; introduces models such as Laguerre and iterated tessellations; and presents theoretical results. Statistics for planar point processes are introduced, and the text also includes a new section on random geometrical graphs and random networks"--
Note:
Revision of: Stochastic geometry and its applications / Dietrich Stoyan, Wilfrid S. Kendall, Joseph Mecke. -- 2nd ed. -- ©1995
,
Includes bibliographical references and indexes
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Stochastic Geometry and its Applications; Contents; Foreword to the first edition; From the preface to the first edition; Preface to the second edition; Preface to the third edition; Notation; 1 Mathematical foundations; 1.1 Set theory; 1.2 Topology in Euclidean spaces; 1.3 Operations on subsets of Euclidean space; 1.4 Mathematical morphology and image analysis; 1.5 Euclidean isometries; 1.6 Convex sets in Euclidean spaces; 1.7 Functions describing convex sets; 1.7.1 General; 1.7.2 Set covariance; 1.7.3 Chord length distribution; 1.7.4 Erosion-dilation functions; 1.8 Polyconvex sets
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1.9 Measure and integration theory2 Point processes I - The Poisson point process; 2.1 Introduction; 2.2 The binomial point process; 2.2.1 Introduction; 2.2.2 Basic properties; 2.2.3 Simulation; 2.3 The homogeneous Poisson point process; 2.3.1 Definition and defining properties; 2.3.2 Characterisation of the homogeneous Poisson point process; 2.3.3 Moments and moment measures; 2.3.4 The Palm distribution of a homogeneous Poisson point process; 2.4 The inhomogeneous and general Poisson point process; 2.5 Simulation of Poisson point processes
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2.5.1 Simulation of a homogeneous Poisson point process2.5.2 Simulation of an inhomogeneous Poisson point process; 2.6 Statistics for the homogeneous Poisson point process; 2.6.1 Introduction; 2.6.2 Estimating the intensity; 2.6.3 Testing the hypothesis of homogeneity; 2.6.4 Testing the Poisson process hypothesis; 3 Random closed sets I - The Boolean model; 3.1 Introduction and basic properties; 3.1.1 Model description; 3.1.2 Applications; 3.1.3 Stationarity and isotropy; 3.1.4 Simulation; 3.1.5 The capacity functional; 3.1.6 Basic characteristics; 3.1.7 Contact distribution functions
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3.2 The Boolean model with convex grains3.2.1 The simplified formula for the capacity functional; 3.2.2 Intensities or densities of intrinsic volumes; 3.2.3 Contact distribution functions; 3.2.4 Morphological functions; 3.2.5 Intersections with linear subspaces; 3.2.6 Formulae for some special Boolean models with isotropic convex grains; 3.3 Coverage and connectivity; 3.3.1 Coverage probabilities; 3.3.2 Clumps; 3.3.3 Connectivity; 3.3.4 Percolation; 3.3.5 Vacant regions; 3.4 Statistics; 3.4.1 General remarks; 3.4.2 Testing model assumptions; 3.4.3 Estimation of model parameters
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3.5 Generalisations and variations3.6 Hints for practical applications; 4 Point processes II - General theory; 4.1 Basic properties; 4.1.1 Introduction; 4.1.2 The distribution of a point process; 4.1.3 Notation; 4.1.4 Stationarity and isotropy; 4.1.5 Intensity measure and intensity; 4.1.6 Ergodicity and central limit theorem; 4.1.7 Contact distributions; 4.2 Marked point processes; 4.2.1 Fundamentals; 4.2.2 Intensity and mark distribution; 4.3 Moment measures and related quantities; 4.3.1 Moment measures; 4.3.2 Factorial moment measures; 4.3.3 Product densities; 4.3.4 The Campbell measure
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4.3.5 The mark correlation function
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Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 1118658248
Additional Edition:
ISBN 1118658256
Additional Edition:
ISBN 1118658221
Additional Edition:
ISBN 9781118658246
Additional Edition:
ISBN 9781118658253
Additional Edition:
ISBN 9781118658222
Additional Edition:
ISBN 9780470664810
Additional Edition:
Erscheint auch als Druck-Ausgabe Stochastic geometry and its applications Chichester [u.a.] : Wiley, 2013 ISBN 9780470664810
Language:
English
Subjects:
Mathematics
Keywords:
Stochastische Geometrie
DOI:
10.1002/9781118658222
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