Stochastic Geometry, Spatial Statistics and Random Fields, 2013
Asymptotic Methods
Lecture Notes in Mathematics Series, Vol. 2068

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.

1 Foundations of stochastic geometry and theory of random sets.- 2 Introduction into integral geometry and stereology.- 3 Spatial point patterns – models and statistics.- 4 Asymptotic methods in statistics of random point processes.- 5 Random tessellations and Cox processes.- 6 Asymptotic methods for random tessellations.- 7 Random polytopes.- 8 Limit theorems in discrete stochastic geometry.- 9 Introduction to random fields.- 10 Central limit theorems for weakly dependent random fields.- 11 Strong limit theorems for increments of random fields.- 12 Geometry of large random trees: SPDE approximation.