Stochastic Geometry, Spatial Statistics and Random Fields: Asymptotic Methods

Description

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 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