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Financial Modeling Under Non-Gaussian Distributions
Practitioners and researchers who have handled financial market data know that asset returns do not behave according to the bell-shaped curve, associated with the Gaussian or normal distribution. Indeed, the use of Gaussian models when the asset return distributions are not normal could lead to a wrong choice of portfolio, the underestimation of extreme losses or mispriced derivative products. Consequently, non-Gaussian models and models based on processes with jumps, are gaining popularity among financial market practitioners. Non-Gaussian distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. One of the main aims is to bridge the gap between the theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models or black boxes. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates. The authors have taken care to make the material accessible to anyone with a basic knowledge of statistics, calculus and probability, while at the same time preserving the mathematical rigor and complexity of the original models. This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.
Category: Business. ISBN: 9781846284199

Stable Non-Gaussian Self-Similar Processes with Stationary Increments
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages.  The authors present a way to describe and classify these processes by relating them to so-called deterministic flows.  The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity.  In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.
Category: Mathematics. ISBN: 9783319623306

Electron Correlation in Molecules ab initio Beyond Gaussian Quantum Chemistry
Electron Correlation in Molecules ab initio Beyond Gaussian Quantum Chemistry presents a series of articles concerning important topics in quantum chemistry, including surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers The volume includes review on all the topics treated by world renown authors and cutting edge research contributions.
Category: Science. ISBN: 9780128030608

Handbook for Applied Modeling: Non-Gaussian and Correlated Data
This compact, entry-level Handbook equips applied practitioners to choose and use core models for real-world data - with R and SAS.
Category: Mathematics. ISBN: 9781107146990

Modelling and Control of Dynamic Systems Using Gaussian Process Models
This monograph opens up new horizons for engineers and researchers inacademia and in industry dealing with or interested in new developments in thefield of system identification and control. It emphasizes guidelines forworking solutions and practical advice for their implementation rather than thetheoretical background of Gaussian process (GP) models. The book demonstratesthe potential of this recent development in probabilistic machine-learningmethods and gives the reader an intuitive understanding of the topic. Thecurrent state of the art is treated along with possible future directions forresearch. Systems control design relies on mathematical models and these may bedeveloped from measurement data. This process of system identification, whenbased on GP models, can play an integral part of control design in data-basedcontrol and its description as such is an essential aspect of the text. Thebackground of GP regression is introduced first with system identification andincorporation of prior knowledge then leading into full-blown control. The bookis illustrated by extensive use of examples, line drawings, and graphicalpresentation of computer-simulation results and plant measurements. Theresearch results presented are applied in real-life case studies drawn fromsuccessful applications including: a gasliquid separator control; urban-traffic signal modelling and reconstruction; and prediction of atmospheric ozone concentration. A MATLAB  toolbox, for identification and simulation ofdynamic GP models is provided for download.
Category: Technology. ISBN: 9783319210209

Stochastic Analysis for Gaussian Random Processes and Fields
Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs). The book begins with preliminary results on covariance and associated RKHS before introducing the Gaussian process and Gaussian random fields. The authors use chaos expansion to define the Skorokhod integral, which generalizes the It integral. They show how the Skorokhod integral is a dual operator of Skorokhod differentiation and the divergence operator of Malliavin. The authors also present Gaussian processes indexed by real numbers and obtain a KallianpurStriebel Bayes' formula for the filtering problem. After discussing the problem of equivalence and singularity of Gaussian random fields (including a generalization of the Girsanov theorem), the book concludes with the Markov property of Gaussian random fields indexed by measures and generalized Gaussian random fields indexed by Schwartz space. The Markov property for generalized random fields is connected to the Markov process generated by a Dirichlet form.
Category: Mathematics. ISBN: 9781498707817

Detection of Random Signals in Dependent Gaussian Noise
The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with Gaussian noise. To facilitate comprehension the text is divided into three broad areas reproducing kernel Hilbert spaces, Cramr-Hida representations and stochastic calculus for which a somewhat different approach was used than in their usual stand-alone context. One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis. The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text will be useful for graduate students and researchers alike in the fields of engineering, mathematics and statistics.
Category: Mathematics. ISBN: 9783319223148

CRC Handbook of Tables for Order Statistics from Inverse Gaussian Distributions with Applications
First derived within the context of life-testing, inverse Gaussian distribution has become one of the most important and widely employed distributions, and is often used to model the lifetimes of components. It is also used as a model in many varied applications, including fatigue analysis, economic prediction analysis, and the analysis of extreme events such as rainfall and flood levels. The interesting features and properties of this distribution make it an important and realistic model in a variety of problems across numerous disciplines. Because of the broad range of applications, this handbook will be useful not only to members of the statistical community but will also appeal to applied scientists, engineers, econometricians, and anyone who desires a thorough evaluation of this important topic.
Category: Mathematics. ISBN: 9780849331183

Bipartite Graphs and their Applications
This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.
Category: Mathematics. ISBN: 9780521593458

Quantum Information Ii
This volume constitutes the proceedings of the Second International Conference on Quantum Information, held at Meijo University, Japan, in 1999. Topics addressed include: CKS-space in terms of growth functions; Gaussian processes and Gaussian random fields; and more.
Category: Science. ISBN: 9789810243173
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