Matrix-analytic Methods in Stochastic Models

Vladimir Gribov was one of the founding fathers of high-energy elementary particle physics. This book derives from a lecture course he delivered to graduate students in the 1970s. It thus provides today's graduate students and researchers with the opportunity to learn from the teaching of one of the twentieth century's greatest physicists. Its content is still deeply relevant to modern research, for example exploring properties of the relativistic theory of hadron interactions in a domain of peripheral collisions and large distances that quantum chromodynamics has barely approached. It covers a combination of topics not treated elsewhere, whilst remaining self-contained and thus accessible at graduate level. In guiding the reader, step-by-step, from the basics of quantum mechanics and relativistic kinematics to the most challenging problems of high-energy hadron interactions with simplifying models and physical analogies, it demonstrates general methods of addressing difficult problems

Written to complement the second edition of best-selling textbook Introductory Econometrics for Finance, this book provides a comprehensive introduction to the use of the Regression Analysis of Time Series (RATS) software for modelling in finance and beyond. It provides numerous worked examples with carefully annotated code and detailed explanations of the outputs, giving readers the knowledge and confidence to use the software for their own research and to interpret their own results. A wide variety of important modelling approaches are covered, including such topics as time-series analysis and forecasting, volatility modelling, limited dependent variable and panel methods, switching models and simulations methods. The book is supported by an accompanying website containing freely downloadable data and RATS instructions.

Written to complement the second edition of best-selling textbook Introductory Econometrics for Finance, this book provides a comprehensive introduction to the use of the Regression Analysis of Time Series (RATS) software for modelling in finance and beyond. It provides numerous worked examples with carefully annotated code and detailed explanations of the outputs, giving readers the knowledge and confidence to use the software for their own research and to interpret their own results. A wide variety of important modelling approaches are covered, including such topics as time-series analysis and forecasting, volatility modelling, limited dependent variable and panel methods, switching models and simulations methods. The book is supported by an accompanying website containing freely downloadable data and RATS instructions.

Statistical ideas and methods underlie just about every aspect of modern life. From randomized clinical trials in medical research, to statistical models of risk in banking and hedge fund industries,

Weaver (learning and information services, U. of Cumbria, UK) compiles 13 chapters that outline methods and models to help librarians, faculty, and staff in higher education adapt their learning suppo

The authors of this tract present a treatment of generalised Clifford parallelism within the framework of complex projective geometry. After a brief survey of the necessary preliminary material, the principal properties of systems of mutually Clifford parallel spaces are developed, centred round discussion of an extended form of the Hurwitz - Radon matrix equations. Later chapters deal with methods for the construction and representation of such systems. Much of the work in the tract is previously unpublished. Some emphasis has been placed throughout on special cases (particularly on the exceptionally interesting parallelisms that exist in spaces of seven and fifteen dimensions). Numerous exercises give the reader a clear insight into the fresh ideas presented. The tract will be of interest to advanced undergraduates and graduates with special interests in algebraic and projective geometry or in the geometry of matrices.

Highlighting modern computational methods, Applied Stochastic Modelling, Second Edition provides students with the practical experience of scientific computing in applied statistics through a range of

Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. In order to solve these models, economists need to use many mathematical tools. This book presents va

The book contains papers that focus explicitly on the last achievements (methods, algorithms, models, systems) with respect to the Third Dimension. Motivated by the rapid developments in 3D, the organ

Stochastic process models are a kind of mathematics that offers enormous opportunities for application to a wide range of problems in the real world, says Solberg (Purdue U.), but almost no one knows

Vibration problems arise in the design of almost all engineering machinery and structures. Many of these problems are extremely complex but their solution is essential if a safe and satisfactory design is to be achieved. The equations of motion are often insoluble by the classical methods of the calculus and so it is necessary to approximate on order to reduce them to a set of linear equations. The use of matrices simplifies the solution of sets of linear equations. This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades,

Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathemat

An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black–Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and martingale approaches. This second edition contains many more worked examples and over 200 exercises with detailed solutions. Extensive appendices provide a guide to jargon, a recap of the elements of probability theory, and a collection of computer projects. The author brings to this book a blend of practical experience and rigorous mathematical background and supplies here the working knowledge needed to b

This volume of essays reflects the increasing breadth and scope of Bach research. The fifteen essays by American and European scholars address a wide range of topics and issues: Magnificat, Cantata, and Passion; Parody and Genre; The Well-Tempered Clavier; and Transmission and Reception. Many of the authors focus on works which due to the Bach chronology - can now be examined in a fresh light. Seen as a whole, the essays combine source - critical and analytic methods with historical and theological interpretation to consider problems of genesis and style, as well as questions of transmission and reception.

Longitudinal Analysis of Labor Market Data presents a set of papers by leading scholars on methods for analysing the longitudinal data that is available on numerous topics of interest to social scientists. Because many sources of longitudinal data record labour market phenomena such as unemployment, labour supply, earnings mobility, job turnover and participation in training programmes, all of the papers collected in this volume focus on models of the labour market. The main methodological points, however, are more general and apply to such diverse areas as demography, life science analysis and training evaluation, to name only a few, potential avenues of application. The book contains important methodological contributions to the emerging field of longitudinal analysis and is of interest to a wide range of social scientists.

Stochastic resonance has been observed in many forms of systems, and has been hotly debated by scientists for over 30 years. Applications incorporating aspects of stochastic resonance may yet prove revolutionary in fields such as distributed sensor networks, nano-electronics, and biomedical prosthetics. Ideal for researchers in fields ranging from computational neuroscience through to electronic engineering, this book addresses in detail various theoretical aspects of stochastic quantization, in the context of the suprathreshold stochastic resonance effect. Initial chapters review stochastic resonance and outline some of the controversies and debates that have surrounded it. The book then discusses suprathreshold stochastic resonance, and its extension to more general models of stochastic signal quantization. Finally, it considers various constraints and tradeoffs in the performance of stochastic quantizers, before culminating with a chapter in the application of suprathreshold stochas

This book deals in a concise format with the methods used to develop mathematical models for water and wastewater treatment. It provides a systematic approach to mass balances, transport and transform

This introduction to general equilibrium modelling takes an integrated approach to the analysis of macroeconomics and finance. It provides students, practitioners, and policymakers with an easily accessible set of tools that can be used to analyze a wide range of economic phenomena. Key features: • Provides a consistent framework for understanding dynamic economic models • Introduces key concepts in finance in a discrete time setting • Develops simple recursive approach for analyzing a variety of problems in a dynamic, stochastic environment • Sequentially builds up the analysis of consumption, production, and investment models to study their implications for allocations and asset prices • Reviews business cycle analysis and the business cycle implications of monetary and international models • Covers latest research on asset pricing in overlapping generations models and on models with borrowing constraints and transaction costs • Includes end-of-chapter exercises allowing readers to m

This introduction to general equilibrium modelling takes an integrated approach to the analysis of macroeconomics and finance. It provides students, practitioners, and policymakers with an easily accessible set of tools that can be used to analyze a wide range of economic phenomena. Key features: • Provides a consistent framework for understanding dynamic economic models • Introduces key concepts in finance in a discrete time setting • Develops simple recursive approach for analyzing a variety of problems in a dynamic, stochastic environment • Sequentially builds up the analysis of consumption, production, and investment models to study their implications for allocations and asset prices • Reviews business cycle analysis and the business cycle implications of monetary and international models • Covers latest research on asset pricing in overlapping generations models and on models with borrowing constraints and transaction costs • Includes end-of-chapter exercises allowing readers to m

This textbook describes some of the most effective and straightforward quantitative techniques for modeling Earth surface processes. By emphasizing a core set of equations and solution techniques, the book presents state-of-the-art models currently employed in Earth surface process research, as well as a set of simple but practical research tools. Detailed case studies demonstrate application of the methods to a wide variety of processes including hillslope, fluvial, aeolian, glacial, tectonic, and climatic systems. Exercises at the end of each chapter begin with simple calculations and then progress to more sophisticated problems that require computer programming. All the necessary computer codes are available online at www.cambridge.org/9780521855976. Assuming some knowledge of calculus and basic programming experience, this quantitative textbook is designed for advanced geomorphology courses and as a reference book for professional researchers in Earth and planetary science looking

Exponential smoothing methods have been around since the 1950s, and are still the most popular forecasting methods used in business and industry. However, a modeling framework incorporating stochastic

This study introduces 'time-specific' analysis of economic processes. Economic processes are conventionally analysed from one point in time to another over a series of time units - days, weeks, or years. By contrast, these time-specific models focus on the temporal character of events within the unit time - their timing, duration, and sequence - utilizing the information that is lost in the macroscopic time perspective of standard economic theory. What time-specific analysis reveals are economic and technological characteristics of goods and services - prices and cost behaviour and temporal mobility or immobility within the unit time - that affect capital productivity and its utilization, optimal schedules of production, work, and consumption, least-cost methods of producing time-shaped outputs, and efficient welfare-maximizing behavior in time-specific, including peak-load, markets.

Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical l

Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer? Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled, with discussions of frequentist and Bayesian methods; model averaging schemes are presented. Real-data examples are complemented by derivations providing deeper insight into the methodology, and instructive exercises build familiarity with the methods. The companion website features Data sets and R code.

A definitive, authoritative and up-to-date resource for anyone interested in the theories, models and assessment methods used for understanding the many factes of Human personality and individual dif

A definitive, authoritative and up-to-date resource for anyone interested in the theories, models and assessment methods used for understanding the many factes of Human personality and individual dif

This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9781107407350.

This book presents state of the art methods for accommodating model uncertainty in random effects and latent variable models. It is divided into four sections featuring articles by experts in the vari

Ecological Models and Data in R is the first truly practical introduction to modern statistical methods for ecology. In step-by-step detail, the book teaches ecology graduate students and researchers

This book develops dynamic economic models using the perspective and analytic framework provided by psychological learning theory. This framework is used to resolve apparent contradictions between optimization theory, which lies at the heart of all modern economic theory, and day-to-day evidence that short-run economic behaviour cannot reasonably be described solely as the outcome of efficiently implemented self-interest. The author applies this viewpoint to a number of problem areas in which literal applications of maximization theory have not usually proved to be satisfactory. These include analyses of decision-making under uncertainty and gambling behaviour, the role of consumer-oriented advertising in influencing behaviour, the persistence of price dispersions in markets, and inflation.

A variety of analytic methods are described and evaluated through such case studies as winners and losers from trade reform in Morocco, the social impact of the Indonesian financial crisis, poverty al

The subject of analysis on Lie groups comprises an eclectic group of topics which can be treated from many different perspectives. This self-contained text concentrates on the perspective of analysis, to the topics and methods of non-commutative harmonic analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author avoids unessential technical discussions and instead describes in detail many interesting examples, including formulae which have not previously appeared in book form. Topics covered include the Haar measure and invariant integration, spherical harmonics, Fourier analysis and the heat equation, Poisson kernel, the Laplace equation and harmonic functions. Perfect for advanced undergraduates and graduates in geometric analysis, harmonic analysis and representation theory, the tools developed will also be useful for specialists in stochastic calculation and the statisticians. With numerous exercises and worked examples, the text is i

Markov chains are an important idea, related to random walks, which crops up widely in applied stochastic analysis. They are used, for example, in performance modelling and evaluation of computer networks, queuing networks, and telecommunication systems. The main point of the present book is to provide methods, based on the construction of Lyapunov functions, of determining when a Markov chain is ergodic, null recurrent, or transient. These methods can also be extended to the study of questions of stability. Of particular concern are reflected random walks and reflected Brownian motion. The authors provide not only a self-contained introduction to the theory but also details of how the required Lyapunov functions are constructed in various situations.

In recent years, the study of bone cells and tissues at the cellular and molecular levels in a variety of models has revolutionized the field. In Osteoporosis: Methods and Protocols, leading scientis

This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology, and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.

This book represents a comprehensive examination of interest-group politics in France. Rather than the narrow case studies usually employed to study group politics, the book focuses on the overall pattern of interaction between interest groups and government. Drawing upon extensive interviews with French interest-group leaders and politicians, Wilson examines the structures and methods of group politics, the perspectives and attitudes of group leaders, and the place of interest groups in the broader pattern of French politics. He concludes that neither of the two major conceptualizations of interest-group/government relations is adequate to explain group politics in France. He suggests that the French state is much more powerful than recognized by these or other models of interest-group politics. Political influence is difficult for groups to develop and, once achieved, is fleeting. Consequently, groups engage in a wide range of activities, some of which are pluralist, others corporati

Currency crises in Europe and Mexico during the 1990s provided stark reminders of the importance and the fragility of international financial markets. These experiences led some commentators to conclude that open international capital markets are incompatible with financial stability. But the pre-1914 gold standard is an obvious challenge to the notion that open capital markets are sources of instability. To deepen our understanding of how this system worked, this volume draws together recent research on the gold standard. Theoretical models are used to guide qualitative discussions of historical experience, while econometric methods are used to help the historical data speak clearly. The result is an overview of the gold standard, a survey of the relevant applied research in international macroeconomics, and a demonstration of how the past can help to inform the present.

Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.