Stochastic Geometry, Spatial Statistics and Random Fields: Asymptotic Methods / Edition 1

by Evgeny Spodarev

Overview

This volume provides a modern introduction to shastic 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.

Product Details

ISBN-13:	9783642333040
Publisher:	Springer Berlin Heidelberg
Publication date:	02/06/2013
Series:	Lecture Notes in Mathematics , #2068
Edition description:	2013
Pages:	446
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 Foundations of shastic 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 shastic 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.