Domain of Attraction
Domain of Attraction

Author: Graziano Chesi

Publisher: Springer Science & Business Media

Published: 2011-08-21

Total Pages: 293

ISBN-13: 0857299581

DOWNLOAD EBOOK

For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.

Domain of Attraction
Domain of Attraction

Author: Graziano Chesi

Publisher: Springer

Published: 2011-08-31

Total Pages: 293

ISBN-13: 085729959X

DOWNLOAD EBOOK

For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.

Statistical Extremes and Applications
Statistical Extremes and Applications

Author: J. Tiago de Oliveira

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 690

ISBN-13: 9401730695

DOWNLOAD EBOOK

The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.

An Intermediate Course in Probability
An Intermediate Course in Probability

Author: Allan Gut

Publisher: Springer Science & Business Media

Published: 2009-06-06

Total Pages: 310

ISBN-13: 1441901620

DOWNLOAD EBOOK

This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.

Operational Risk
Operational Risk

Author: Harry H. Panjer

Publisher: John Wiley & Sons

Published: 2006-10-13

Total Pages: 460

ISBN-13: 0470051302

DOWNLOAD EBOOK

Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.

Nonlinear and Optimal Control Systems
Nonlinear and Optimal Control Systems

Author: Thomas L. Vincent

Publisher: John Wiley & Sons

Published: 1997-06-23

Total Pages: 584

ISBN-13: 9780471042358

DOWNLOAD EBOOK

Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.

Laws Of Small Numbers
Laws Of Small Numbers

Author: Michael Falk

Publisher: Springer Science & Business Media

Published: 2004

Total Pages: 396

ISBN-13: 9783764324162

DOWNLOAD EBOOK

Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages. Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.

Statistics of Extremes
Statistics of Extremes

Author: Jan Beirlant

Publisher: John Wiley & Sons

Published: 2004-10-15

Total Pages: 516

ISBN-13: 9780471976479

DOWNLOAD EBOOK

Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

The Biostatistics of Aging
The Biostatistics of Aging

Author: Gilberto Levy

Publisher: John Wiley & Sons

Published: 2014-04-07

Total Pages: 268

ISBN-13: 1118645855

DOWNLOAD EBOOK

A practical and clarifying approach to aging and aging-related diseases Providing a thorough and extensive theoretical framework, The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness addresses the surprisingly subtlenotion—with consequential biomedical and public health relevance—of what it means for acondition to be related to aging. In this pursuit, the book presents a new quantitative methodto examine the relative contributions of genetic and environmental factors to mortality anddisease incidence in a population. With input from evolutionary biology, population genetics, demography, and epidemiology, this medically motivated book describes an index of aging-relatedness and also features: Original results on the asymptotic behavior of the minimum of time-to-event random variables, which extends those of the classical statistical theory of extreme values A comprehensive and satisfactory explanation based on biological principles of the Gompertz pattern of mortality in human populations The development of an evolution-based model of causation relevant to mortality and aging-related diseases of complex etiology An explanation of how and why the description of human mortality by the Gompertz distribution can be improved upon from first principles The amply illustrated analysis of real-world data, including a program for conducting the analysis written in the freely available R statistical software Technical appendices including mathematical material as well as an extensive and multidisciplinary bibliography on aging and aging-related diseases The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness is an excellent resource for practitioners and researchers with an interest in aging and aging-related diseases from the fields of medicine, biology, gerontology, biostatistics, epidemiology, demography, and public health.