Matrix-analytic Methods in Stochastic Models

Intended for graduate students in mathematics, this textbook is an introduction to probabilistic methods in finance that focuses on stochastic models in real time. It is based on courses taught by the

This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quan

This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quan

This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.

Moving on from earlier stochastic and robust control paradigms, this book introduces the fundamentals of probabilistic methods in the analysis and design of uncertain systems. The use of randomized a

Time series econometrics is a rapidly evolving field. Particularly, the cointegration revolution has had a substantial impact on applied analysis. Hence, no textbook has managed to cover the full range of methods in current use and explain how to proceed in applied domains. This gap in the literature motivates the present volume. The methods are sketched out, reminding the reader of the ideas underlying them and giving sufficient background for empirical work. The treatment can also be used as a textbook for a course on applied time series econometrics. Topics include: unit root and cointegration analysis, structural vector autoregressions, conditional heteroskedasticity and nonlinear and nonparametric time series models. Crucial to empirical work is the software that is available for analysis. New methodology is typically only gradually incorporated into existing software packages. Therefore a flexible Java interface has been created, allowing readers to replicate the applications and

Time series econometrics is a rapidly evolving field. Particularly, the cointegration revolution has had a substantial impact on applied analysis. Hence, no textbook has managed to cover the full range of methods in current use and explain how to proceed in applied domains. This gap in the literature motivates the present volume. The methods are sketched out, reminding the reader of the ideas underlying them and giving sufficient background for empirical work. The treatment can also be used as a textbook for a course on applied time series econometrics. Topics include: unit root and cointegration analysis, structural vector autoregressions, conditional heteroskedasticity and nonlinear and nonparametric time series models. Crucial to empirical work is the software that is available for analysis. New methodology is typically only gradually incorporated into existing software packages. Therefore a flexible Java interface has been created, allowing readers to replicate the applications and

Fundamentals of Seismic Wave Propagation, published in 2004, presents a comprehensive introduction to the propagation of high-frequency body-waves in elastodynamics. The theory of seismic wave propagation in acoustic, elastic and anisotropic media is developed to allow seismic waves to be modelled in complex, realistic three-dimensional Earth models. This book provides a consistent and thorough development of modelling methods widely used in elastic wave propagation ranging from the whole Earth, through regional and crustal seismology, exploration seismics to borehole seismics, sonics and ultrasonics. Particular emphasis is placed on developing a consistent notation and approach throughout, which highlights similarities and allows more complicated methods and extensions to be developed without difficulty. This book is intended as a text for graduate courses in theoretical seismology, and as a reference for all academic and industrial seismologists using numerical modelling methods. Exe

This book provides a new perspective on how events or conditions in environmental space have influences at other places in that space. In the first half of the book, the authors introduce the general question of propagation of ecological influences through environmental space (terrestrial, aquatic and aerial), then lay out a system for its analysis by organization into four components: initiating events or conditions, vectors conducting influences over space, entities that are transported, and the consequences of these propagation processes. Methods of representing environmental heterogeneity and for modeling transport processes are discussed in the context of such propagations. In the second half of the book, properties of eight general transport vectors and examples of transport models in realistic ecological situations are explained. For each of the vectors, a simulation model is provided on a CD included with the book (users require access to ArcView GIS software).

This 2004 volume offers a broad overview of developments in the theory and applications of state space modeling. With fourteen chapters from twenty-three contributors, it offers a unique synthesis of state space methods and unobserved component models that are important in a wide range of subjects, including economics, finance, environmental science, medicine and engineering. The book is divided into four sections: introductory papers, testing, Bayesian inference and the bootstrap, and applications. It will give those unfamiliar with state space models a flavour of the work being carried out as well as providing experts with valuable state of the art summaries of different topics. Offering a useful reference for all, this accessible volume makes a significant contribution to the literature of this discipline.

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields.

This book provides a pedagogical introduction to the perturbative and non-perturbative aspects of quantum chromodynamics (QCD). Introducing the basic theory and recent advances in QCD, it also reviews the historical development of the subject, covering pre-QCD ideas of strong interactions such as the quark and parton models, the notion of colours and the S-matrix approach. The author then discusses gauge theory, techniques of dimensional regularization and renormalization, deep inelastic scattering and hard processes in hadron collisions, hadron jets and e+e– annihilations. Other topics include power corrections and the technologies of the Shifman-Vainshtein-Zakharov operating product expansion. The final parts of the book are devoted to modern non-perturbative approaches to QCD and the phenomenological aspects of QCD spectral sum rules. The book will be a valuable reference for graduate students and researchers in high-energy particle and nuclear physics, both theoretical and experime

First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more referen

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly fr

Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make

Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make

This is a practically oriented introduction to the realiability of measurements. One of the implicit themes is that the measurement models and the statistical methods used in the assessment of accurac

This book covers at an advanced level mathematical methods for analysis of telecommunication networks. The book concentrates on various call models used in telecommunications such as quality of servic

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

This book discusses recent research in the theoretical foundations of several subjects of importance for the design of hardware, and for computer science in general. The physical technologies of very large scale integration (VLSI) are having major effects on the electronic industry. The potential diversity and complexity of digital systems have begun a revolution in the technologies of digital design, involving the application of concepts and methods to do with algorithms and programming. In return, the problems of VLSI design have led to new subjects becoming of importance in computer science. Topics covered in this volume include: models of VLSI complexity; complexity theory; systolic algorithm design; specification theory; verification theory; design by stepwise refinement and transformations. A thorough literature survey with an exhaustive bibliography is also included. The book has grown from a workshop held at the Centre for Theoretical Computer Science at Leeds University and or

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Dynamic stochastic general equilibrium (DSGE) models have begun to dominate the field of macroeconomic theory and policy-making. These models describe the evolution of macroeconomic activity as a recursive sequence of outcomes based upon the optimal decision rules of rational households, firms and policy-makers. Whilst posing a micro-founded dynamic optimisation problem for agents under uncertainty, such models have been shown to be both analytically tractable and sufficiently rich for meaningful policy analysis in a wide class of macroeconomic problems, for example, monetary and fiscal policy, economic cycles and growth and capital flows. This volume collects specially commissioned papers from leading researchers, which pull together some of the key results in diverse areas. This book will promote research using optimising models and inform researchers, post-graduate students and economists in policy-oriented organisations of some of the key findings and policy implications.

Dynamic stochastic general equilibrium (DSGE) models have begun to dominate the field of macroeconomic theory and policy-making. These models describe the evolution of macroeconomic activity as a recursive sequence of outcomes based upon the optimal decision rules of rational households, firms and policy-makers. Whilst posing a micro-founded dynamic optimisation problem for agents under uncertainty, such models have been shown to be both analytically tractable and sufficiently rich for meaningful policy analysis in a wide class of macroeconomic problems, for example, monetary and fiscal policy, economic cycles and growth and capital flows. This volume collects specially commissioned papers from leading researchers, which pull together some of the key results in diverse areas. This book will promote research using optimising models and inform researchers, post-graduate students and economists in policy-oriented organisations of some of the key findings and policy implications.

The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more tradi

This book presents an approach to introductory graduate courses on atomic structure. The author's approach utilizes conceptually powerful semiclassical modeling methods, and demonstrates the degree to which the Maslov-indexed EBK quantization elucidates the quantum mechanical formulation of level energies and lifetimes. It merges this with an update and extension of semiempirical data systematizations developed by Bengt Edlén to describe complex atoms, and adapts them to include the specification of lifetimes. The text emphasizes the historical basis of the nomenclature and methodologies of spectroscopy. However, interaction mechanisms are presented deductively, based on quantum mechanical and field theoretical models, rather than tracing their indirect paths of discovery. Many worked examples provide applications to areas such as astrophysics, hyperfine structure, and coherent anisotropic excitation. The book presents a firm foundation for specialists in atomic physics, as well as a c

This book presents the current state of the art in computational models for turbulent reacting flows, and analyzes carefully the strengths and weaknesses of the various techniques described. The focus is on formulation of practical models as opposed to numerical issues arising from their solution. A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed. It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy. Models based on direct closures for the chemical source term as well as transported PDF methods are covered in detail. An introduction to the theory of turbulent and turbulent scalar transport is provided for completeness. The book is aimed at chemical, mechanical, and aerospace engineers in academia and industry, as well as developers of computational fluid dynamics codes for reacting flows.

This book presents an approach to introductory graduate courses on atomic structure. The author's approach utilizes conceptually powerful semiclassical modeling methods, and demonstrates the degree to which the Maslov-indexed EBK quantization elucidates the quantum mechanical formulation of level energies and lifetimes. It merges this with an update and extension of semiempirical data systematizations developed by Bengt Edlén to describe complex atoms, and adapts them to include the specification of lifetimes. The text emphasizes the historical basis of the nomenclature and methodologies of spectroscopy. However, interaction mechanisms are presented deductively, based on quantum mechanical and field theoretical models, rather than tracing their indirect paths of discovery. Many worked examples provide applications to areas such as astrophysics, hyperfine structure, and coherent anisotropic excitation. The book presents a firm foundation for specialists in atomic physics, as well as a c

This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.

This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

This book develops the use of Monte Carlo methods in finance, and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts.

The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers.

Lande (biology, U. of California, San Diego) introduces biological concepts and mathematical methods that have proven useful in analyzing stochastic population dynamics, using field data from bird, ma

Complex variables provide powerful methods for attacking problems that can be very difficult to solve in any other way, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann–Hilbert problems. The authors provide an extensive array of applications, illustrative examples and homework exercises. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.

Introduction to sequential decision processes covers use of dynamic programming in studying models of resource allocation, methods for approximating solutions of control problems in continuous time, p

* Presents theoretical models for interpreting and predicting solubilities in solutions.* Evaluates the collection techniques used to obtain solubility data and presents the most appropriate methods.*

Dynamics of the Atmosphere consists of two parts: the first presenting the mathematical tools needed for a thorough understanding of the topics covered in the second part of the book. The second part begins with the derivation of the equation describing the atmospheric motion on the rotating earth. Subjects tackled in subsequent chapters include kinematics of the atmosphere (including vorticity and circulation theorems), wave motion in the atmosphere, inertial and dynamic stability, and turbulent systems in the atmosphere. Finally, newer methods of weather prediction, such as the spectral technique and the stochastic dynamic method, are introduced in order to demonstrate their potential for extending the forecasting range. Complete with numerous exercise sets and solutions, this textbook has been written for advanced undergraduate and graduate students of meteorology and other related sciences. It may also be used as a reference source by professional meteorologists and researchers in

This book discusses how citizens can participate more effectively in sustainability science and environmental policy debates. It discusses designs for participatory procedures, and experiences of their application to issues of global change. While the focus is on citizen participation, the involvement of specific stakeholders - including water managers and venture capitalists - is also addressed. The book describes how focus group methods were combined with the interactive use of computer models into new forms of participation, tested with six hundred citizens. The results are discussed in relation to other important topics, including greenhouse gas and water management. By combining this with an examination of issues of interactive governance and developing country participation, the book provides state-of-the-art, practical insights for students, researchers and policy makers alike.

This book discusses how citizens can participate more effectively in sustainability science and environmental policy debates. It discusses designs for participatory procedures, and experiences of their application to issues of global change. While the focus is on citizen participation, the involvement of specific stakeholders - including water managers and venture capitalists - is also addressed. The book describes how focus group methods were combined with the interactive use of computer models into new forms of participation, tested with six hundred citizens. The results are discussed in relation to other important topics, including greenhouse gas and water management. By combining this with an examination of issues of interactive governance and developing country participation, the book provides state-of-the-art, practical insights for students, researchers and policy makers alike.

Dynamics of the Atmosphere consists of two parts: the first presenting the mathematical tools needed for a thorough understanding of the topics covered in the second part of the book. The second part begins with the derivation of the equation describing the atmospheric motion on the rotating earth. Subjects tackled in subsequent chapters include kinematics of the atmosphere (including vorticity and circulation theorems), wave motion in the atmosphere, inertial and dynamic stability, and turbulent systems in the atmosphere. Finally, newer methods of weather prediction, such as the spectral technique and the stochastic dynamic method, are introduced in order to demonstrate their potential for extending the forecasting range. Complete with numerous exercise sets and solutions, this textbook has been written for advanced undergraduate and graduate students of meteorology and other related sciences. It may also be used as a reference source by professional meteorologists and researchers in