Point Processes Analysis

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure…

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis.

Authors: Itô, Kiyosi
Gives a beautiful elementary treatment of general Poisson point processes in Chapter 1, especially recommended for beginners
Shows how the notion of Poisson point processes with values in a function space of paths called excursions plays a key role in an extension problem of Markov processes in Chapter 2
Demonstrates how the general theory in Chapter 2 can answer completely the extension problem for the minimal diffusion on [0, ∞) with an exit boundary 0[/i]

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics.