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.

List of contents

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.

Summary

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.

Product details

• Assisted by: Evgen Spodarev (Editor), Evgeny Spodarev (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 09.08.2012
• EAN: 9783642333040
• ISBN: 978-3-642-33304-0
• No. of pages: 446
• Dimensions: 156 mm x 26 mm x 236 mm
• Weight: 707 g
• Illustrations: XXIV, 446 p. 105 illus., 27 illus. in color.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; B, Statistics, Mathematics and Statistics, Statistical Theory and Methods, Probability Theory and Stochastic Processes, Discrete Mathematics, Probability & statistics, Discrete geometry, Convex and Discrete Geometry, Convex geometry, Probabilities, Stochastics, Probability Theory