Discrete phenomena are an important aspect of various complex systems, acting both as underlying driving mechanisms and as manifestations of diverse behaviours. However, the characterisation of these discrete phenomena requires models that go beyond those featured in existing books.
Largely concerned with mathematical models used to describe time-varying populations and series of events, The Dynamics of Discrete Populations and Series of Events demonstrates how analytical tools are used to develop, simulate, and solve discrete stochastic models. It provides an understanding of the effect of the competing processes governing the changing number of individuals present in a population, and shows how relatively simple models can be used to generate a wide range of behaviours.
Introduction. Statistical Preliminaries. Markovian Population Processes. The Birth–Death–Immigration Process. Population Processes Exhibiting Sub-Poisson Fluctuations and Odd–Even Effects. The Death–Multiple Immigration Process. Stable Processes and Series of Events. Coupled Processes. Doubly Stochastic Processes. Level Crossings of a Continuous Process. Simulation Techniques.