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The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting o

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which th

An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by

A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical