Download or read book Simulation and Chaotic Behavior of Alpha stable Stochastic Processes written by Aleksand Janicki and published by CRC Press. This book was released on 1993-11-16 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.

Download or read book Simulation and Chaotic Behavior of Alpha stable Stochastic Processes written by Aleksand Janicki and published by CRC Press. This book was released on 2021-07-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.

Download or read book Stochastic Process Limits written by Ward Whitt and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews

Download or read book Stochastic Analysis of Scaling Time Series written by François G. Schmitt and published by Cambridge University Press. This book was released on 2016-01-07 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough understanding of the techniques used to retrieve multi-scale information from turbulent and complex systems, with case studies.

Download or read book Numerical Solution of Stochastic Differential Equations with Jumps in Finance written by Eckhard Platen and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Download or read book Advances in Heavy Tailed Risk Modeling written by Gareth W. Peters and published by John Wiley & Sons. This book was released on 2015-05-21 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distribution approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modeling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.

Download or read book Data Analysis and Decision Support written by Daniel Baier and published by Springer Science & Business Media. This book was released on 2005-07-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a great privilege and pleasure to write a foreword for a book honor ing Wolfgang Gaul on the occasion of his sixtieth birthday. Wolfgang Gaul is currently Professor of Business Administration and Management Science and the Head of the Institute of Decision Theory and Management Science, Faculty of Economics, University of Karlsruhe (TH), Germany. He is, by any measure, one of the most distinguished and eminent scholars in the world today. Wolfgang Gaul has been instrumental in numerous leading research initia tives and has achieved an unprecedented level of success in facilitating com munication among researchers in diverse disciplines from around the world. A particularly remarkable and unique aspect of his work is that he has been a leading scholar in such diverse areas of research as graph theory and net work models, reliability theory, stochastic optimization, operations research, probability theory, sampling theory, cluster analysis, scaling and multivariate data analysis. His activities have been directed not only at these and other theoretical topics, but also at applications of statistical and mathematical tools to a multitude of important problems in computer science (e.g., w- mining), business research (e.g., market segmentation), management science (e.g., decision support systems) and behavioral sciences (e.g., preference mea surement and data mining). All of his endeavors have been accomplished at the highest level of professional excellence.

Download or read book Financial Models with Levy Processes and Volatility Clustering written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Download or read book Change Of Time And Change Of Measure written by Ole E Barndorff-nielsen and published by World Scientific Publishing Company. This book was released on 2010-11-04 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. It is invaluable as a textbook for graduate-level courses and students or a handy reference for researchers and practitioners in financial mathematics and econometrics.

Download or read book Applications in Physics Part B written by Vasily E. Tarasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

Download or read book Stochastic versus Deterministic Systems of Differential Equations written by G. S. Ladde and published by CRC Press. This book was released on 2003-12-05 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/fluctuations and parameter uncertainties both deterministic and stochastic.

Download or read book Handbook Of Heavy tailed Distributions In Asset Management And Risk Management written by Michele Leonardo Bianchi and published by World Scientific. This book was released on 2019-03-08 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.

Download or read book Applied Functional Analysis written by Abul Hasan Siddiqi and published by CRC Press. This book was released on 2003-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.

Download or read book The Mathematical Theory of Tone Systems written by Jan Haluska and published by CRC Press. This book was released on 2003-12-19 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of examples of past and prevalent tone systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems. Well Tempered Systems, Ptolemy Systems, and more. Appendices include extended lists of tone systems and a catalogue of historical organs with subsemitones.

Download or read book Univariate Stable Distributions written by John P. Nolan and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.

Download or read book Handbook of Computational Statistics written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2012-07-06 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.

Download or read book Advances in the Theory and Applications of Non integer Order Systems written by Wojciech Mitkowski and published by Springer Science & Business Media. This book was released on 2013-06-03 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes, acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.