Ebook: Stochastic Geometry, Spatial Statistics and Random Fields: Asymptotic Methods

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

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This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

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This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Content:
Front Matter....Pages i-xxiv
Foundations of Stochastic Geometry and Theory of Random Sets....Pages 1-20
Introduction into Integral Geometry and Stereology....Pages 21-48
Spatial Point Patterns: Models and Statistics....Pages 49-114
Asymptotic Methods in Statistics of Random Point Processes....Pages 115-150
Random Tessellations and Cox Processes....Pages 151-182
Asymptotic Methods for Random Tessellations....Pages 183-204
Random Polytopes....Pages 205-238
Limit Theorems in Discrete Stochastic Geometry....Pages 239-275
Introduction to Random Fields....Pages 277-335
Central Limit Theorems for Weakly Dependent Random Fields....Pages 337-383
Strong Limit Theorems for Increments of Random Fields....Pages 385-398
Geometry of Large Random Trees: SPDE Approximation....Pages 399-420
Back Matter....Pages 421-448

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This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Content:
Front Matter....Pages i-xxiv
Foundations of Stochastic Geometry and Theory of Random Sets....Pages 1-20
Introduction into Integral Geometry and Stereology....Pages 21-48
Spatial Point Patterns: Models and Statistics....Pages 49-114
Asymptotic Methods in Statistics of Random Point Processes....Pages 115-150
Random Tessellations and Cox Processes....Pages 151-182
Asymptotic Methods for Random Tessellations....Pages 183-204
Random Polytopes....Pages 205-238
Limit Theorems in Discrete Stochastic Geometry....Pages 239-275
Introduction to Random Fields....Pages 277-335
Central Limit Theorems for Weakly Dependent Random Fields....Pages 337-383
Strong Limit Theorems for Increments of Random Fields....Pages 385-398
Geometry of Large Random Trees: SPDE Approximation....Pages 399-420
Back Matter....Pages 421-448
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