The Dynamics of Discrete Populations and Series of Events by Keith Iain Hopcraft Eric Jakeman Kevin D Ridley(pradyutvam2).pdf

January 17, 2014 by CRC Press
Textbook - 223 Pages - 74 B/W Illustrations
ISBN 9781420060676 - CAT# C6067
Series: Graduate Student Series in Physics

Features

Provides an introduction to the stochastic modeling of discrete populations and associated series of events
Presents a comprehensive analysis of the classic problem of the evolution of a population subjected to births, deaths, and immigration, and the process of monitoring such a population, either by counting individuals within the population or individuals that leave the population
Considers less familiar population models which have no continuous counterparts and shows how these may exhibit sub-Poisson traits and odd/even effects in their fluctuations Develops models of populations subject to simultaneous multiple immigrations and shows how these can be used to produce a model with any desired equilibrium distribution. Application to the important class of stable distributions is examined in detail
Shows how discrete series of events can arise from level crossings of continuous processes, and how the statistics of these events can be characterized
Presents methods for numerical simulation of dynamic populations, giving examples of algorithms that can be used to simulate most of the processes considered in the book
Includes a bibliography for further reading as well as problems to encourage hands-on practice with the techniques, further develop ideas from the text, and derive results from technical literature
Summary

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.