The dynamics of discrete populations and series of events. ([2014])

• Record Type: Book
• Further Information: Note: Keith Iain Hopcraft, University of Nottingham, UK ; Eric Jakeman, University of Nottingham, UK ; Kevin D. Ridley, Consultant Optical Physicist, UK.
• Other Names: Hopcraft, K. I; Jakeman, E; Ridley, K. D (Kevin Dennis)
• 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
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2014
• Extent: 1 online resource
• Subjects: 519.233; Markov processes; Mathematical statistics; Variables (Mathematics); Markov processes; Mathematical statistics; Variables (Mathematics); Electronic books
• Languages: English
• ISBNs: 9781482227659; 1482227657
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.