The Dynamics of Discrete Populations and Series of Events

The Dynamics of Discrete Populations and Series of Events

by Keith Iain Hopcraft, Eric Jakeman, Kevin D. Ridley
     
 

ISBN-10: 1420060678

ISBN-13: 9781420060676

Pub. Date: 01/29/2014

Publisher: Taylor & Francis

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

Overview

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.

Product Details

ISBN-13:
9781420060676
Publisher:
Taylor & Francis
Publication date:
01/29/2014
Series:
Graduate Student Series in Physics Series
Pages:
223
Product dimensions:
6.10(w) x 9.40(h) x 0.40(d)

Table of Contents

Introduction
References

Statistical Preliminaries
Introduction
Probability Distributions
Moment-Generating Functions
Discrete Processes
Series of Events
Summary
Further Reading

Markovian Population Processes
Introduction
Births and Deaths
Immigration and the Poisson Process
The Effect of Measurement
Correlation of Counts
Summary
Further Reading

The Birth-Death-Immigration Process
Introduction
Rate Equations for the Process
Equation for the Generating Function
General Time-Dependent Solution
Fluctuation Characteristics of a Birth-Death-Immigration Population
Sampling and Measurement Processes
Correlation of Counts
Summary
Further Reading

Population Processes Exhibiting Sub-Poisson Fluctuations and Odd-Even Effects
Introduction
A Limited Birth-Death Process: Binomial Number Fluctuations

The Effect of Monitoring a Limited Birth-Death Process
A Birth Limited Death Immigration Process
The Effect of Monitoring a Birth Limited Death Process
Odd Even Effects in a Population Driven by Immigrant Pairs
Monitoring an Immigrant Pair Death Process
Summary
Further Reading

The Death-Multiple Immigration Process
Introduction
Rate and Generating-Function Equations for the Process
Negative Binomial Fluctuations Revisited
Sampling and Measurement Processes
Time-Dependent Multiple Immigrations
Summary
Further Reading

Stable Processes and Series of Events
Introduction
Discrete Stability
A Discrete Stable Markov Process
Stable Series of Events
Construction of Statistical Measures by Clipping
Summary
Further Reading

Coupled Processes
Introduction
Coupled Death Multiple Immigrations Processes
Properties of Populations Coupled by Multiple Immigrations
Cyclically Coupled Populations
Populations Coupled through Exchange Interactions
Summary
Further Reading

Doubly Stochastic Processes
Introduction
General Statistical Relationships
Commonly Encountered Doubly Stochastic Poisson Processes
Continuous and Discrete Stable Variables
Doubly Stochastic Stable Processes
Summary
Further Reading

Level Crossings of a Continuous Process
Introduction
Generalisation of the Van Vleck Theorem
Crossing Number Statistics of a Differentiable Process
Processes that are Continuous but Not Differentiable
Distribution of Intervals between Zeros
Summary
Further Reading

Simulation Techniques
Introduction
Interevent Intervals
Transformation of Random Variables
Simulating the Death Immigration Process
Extension to More than Two Events
Processes with Multiple Immigrations
Gaussian Random Process
The Doubly Stochastic Poisson Process
Summary
Further Reading

Glossary of Special Functions

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