Matrix-analytic Methods in Stochastic Models

Changes in the shape of the yield curve have traditionally been one of the key macroeconomic indicators of a likely change in economic outlook. However, the recent financial crises have created a challenge to the management of monetary policy, demanding a revision in the way that policymakers model expected changes in the economy. This volume brings together central bank economists and leading academic monetary economists to propose new methods for modelling the behaviour of interest rates. Topics covered include: the analysis and extraction of expectations of future monetary policy and inflation; the analysis of the short-term dynamics of money market interest rates; the reliability of existing models in periods of extreme market volatility and how to adjust them accordingly; and the role of government debt and deficits in affecting sovereign bond yields and spreads. This book will interest financial researchers and practitioners as well as academic and central bank economists.

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the dis

This second edition of Working with Dynamic Crop Models is meant for self-learning by researchers or for use in graduate level courses devoted to methods for working with dynamic models in crop, agric

Direct and to the point, this book from one of the field's leaders covers Brownian motion and stochastic calculus at the graduate level, and illustrates the use of that theory in various application domains, emphasizing business and economics. The mathematical development is narrowly focused and briskly paced, with many concrete calculations and a minimum of abstract notation. The applications discussed include: the role of reflected Brownian motion as a storage model, queuing model, or inventory model; optimal stopping problems for Brownian motion, including the influential McDonald–Siegel investment model; optimal control of Brownian motion via barrier policies, including optimal control of Brownian storage systems; and Brownian models of dynamic inference, also called Brownian learning models or Brownian filtering models.

The book presents a comprehensive overview of modern mathematical concepts, models, methods and tools with applications in computer graphics, computer vision and machine learning.Fifteen topics in mod

The book presents a comprehensive overview of modern mathematical concepts, models, methods and tools with applications in computer graphics, computer vision and machine learning.Fifteen topics in mod

Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.

Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity sci

Statistical Models and Methods for Reliability and Survival Analysis is a compilation of articles by statistical theory experts that explore developments in survival analysis, statistical goodness of

The aim of the book is to give an accessible introduction of mathematical models and signal processing methods in speech and hearing sciences for senior undergraduate and beginning graduate students w

The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and

Advances in social science research methodologies and data analytic methods are changing the way research in information systems is conducted. New developments in statistical software technologies for

This engaging study focuses on the role of assemblies in later Anglo-Saxon politics, challenging and nuancing existing models of the late Anglo-Saxon state. Its ten chapters investigate both traditional constitutional aspects of assemblies - who attended these events, where and when they met, and what business they conducted - and the symbolic and representational nature of these gatherings. Levi Roach takes into account important recent work on continental rulership, and argues that assemblies were not a check on kingship in these years, but rather an essential feature of it. In particular, the author highlights the role of symbolic communication at assemblies, arguing that ritual and demonstration were as important in English politics as they were elsewhere in Europe. Far from being exceptional, the methods of rulership employed by English kings look very much like those witnessed elsewhere on the continent, where assemblies and ritual formed an essential part of the political order.

Silvestrov systematically presents stochastic approximation methods for models of American-type options with general pay-off functions for discrete Markov log-price processes. The discrete-time multiv

In a world in which we are constantly surrounded by data, figures, and statistics, it is imperative to understand and to be able to use quantitative methods. Statistical models and methods are among t

Providing widely used techniques in genetic model systems and many complementing animal models, Brain Development: Methods and Protocols focuses its expert contributions on two key technical aspects o

The parallel developments of the Finite Element Methods in the 1950’s and the engineering applications of stochastic processes in the 1940’s provided a combined numerical analysis tool for the studies

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of di

This book presents new trends in optimization methods that can be used to handle the stochastic, predictive nature of large-scale system problems in power and energy. The author provides decision tool

Presenting probability and statistical methods, simulation techniques, and modeling tools, this book helps students solve problems and make optimal decisions in uncertain conditions, select stochastic

"This book investigates a variety of programming languages used in validating and verifying models in order to assist in their eventual implementation, exploring different methods of evaluating and fo

The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models an

This book presents a broad collection of models and computational methods - from atomistic to continuum - applied to crystal dislocations. Its purpose is to help students and researchers in computatio

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introducti

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange–Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis,

Partial Differential Equations: Topics in Fourier Analysis explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It s

This book presents topics in a single source format using unified spectral theory of computing. With developments of DNS and LES, practitioners are rediscovering waves as important in fluid flows, and capturing these numerically is central to high accuracy computing. Analysis of waves and its use in numerical methods in propagating energy at the right velocity (dispersion effects) and with right amplitude (dissipation) are essential. Most industrial codes using Reynolds-averaged Navier–Stokes equations with turbulence models cannot conceive of capturing waves. The new themes covered in this book are: • Correct error propagation analysis • Practical compact schemes and global analysis tool • Aliasing error and its alleviation • Spurious upstream propagating q-waves • Explanation of the Gibbs phenomenon • New 1D and 2D filters for LES/DNS without SGS modelling • Anisotropic skewed wave propagation • Development and analysis of dispersion relation preservation (DRP) schemes • Flow instabi

This book covers a large spectrum of dynamical models in engineering: discrete and continuous time, deterministic and stochastic, state space and input-output systems. It includes proofs, exercises, a

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on

This book is a major update of novel targets in angiogenesis modulation, including pro- and anti-angiogenesis. There is in-depth coverage of preclinical and clinical methods and models, investigationa

Thorough and informative, this Methods in Molecular Biology? book presents key models used to characterize the tissue-protective actions of cytokines. Offers lists of materials and reagents, step-by-s

The aim of this book is to promote interaction between Engineering, Finance and Insurance, as there are many models and solution methods in common for solving real-life problems in these three topics.

Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and d

Recent decades have brought advances in statistical theory for missing data, which, combined with advances in computing ability, have allowed implementation of a wide array of analyses. In fact, so many methods are available that it can be difficult to ascertain when to use which method. This book focuses on the prevention and treatment of missing data in longitudinal clinical trials. Based on his extensive experience with missing data, the author offers advice on choosing analysis methods and on ways to prevent missing data through appropriate trial design and conduct. He offers a practical guide to key principles and explains analytic methods for the non-statistician using limited statistical notation and jargon. The book's goal is to present a comprehensive strategy for preventing and treating missing data, and to make available the programs used to conduct the analyses of the example dataset.

A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

Age-Period-Cohort Analysis: New Models, Methods, and Empirical Applications is based on a decade of the authors’ collaborative work in age-period-cohort (APC) analysis. Within a single, consistent HAP

Recent decades have brought advances in statistical theory for missing data, which, combined with advances in computing ability, have allowed implementation of a wide array of analyses. In fact, so many methods are available that it can be difficult to ascertain when to use which method. This book focuses on the prevention and treatment of missing data in longitudinal clinical trials. Based on his extensive experience with missing data, the author offers advice on choosing analysis methods and on ways to prevent missing data through appropriate trial design and conduct. He offers a practical guide to key principles and explains analytic methods for the non-statistician using limited statistical notation and jargon. The book's goal is to present a comprehensive strategy for preventing and treating missing data, and to make available the programs used to conduct the analyses of the example dataset.

This is a collection of articles on fundamental physical principles and methods, the topics ranging from matrix models, random surfaces, quantum dots and rings, to black holes, cosmology and testing o