A crash course in stochastic geometry
Adrian J. Baddeley · 2019
This chapter aims to give the reader a rapid introduction to the main ideas of stochastic geometry. It is not a literature review but rather a very selective presentation of some of the key points. Stochastic geometry has applications to digital image analysis, spatial statistics and stereology, and connections with many areas of probability and statistics. Modern stochastic geometry handles random subsets of arbitrary form, for example, the zero set of a random function, or a randomly-generated fractal. The fundamental idea of stochastic geometry is to find connections between geometry and probability, i.e. between the geometrical and probabilistic aspects of random spatial processes. Spatial structure induces stochastic dependence. Weighted distributions are ubiquitous in stochastic geometry. They arise from sampling bias effects, and as conditional or marginal distributions. Independent random variables are common in the study of one-dimensional random processes, but are scarcer in stochastic geometry.