### Non-**Gaussian** Statistical Communication Theory

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The book is based on the observation that communication is the central operation of discovery in all the sciences. In its "active mode" we use it to "interrogate" the physical world, sending appropriate "signals" and receiving nature's "reply". In the "passive mode" we receive nature's signals directly. Since we never know a priori what particular return signal will be forthcoming, we must necessarily adopt a probabilistic model of communication. This has developed over the approximately seventy years since it's beginning, into a Statistical Communication Theory (or SCT). Here it is the set or ensemble of possible results which is meaningful. From this ensemble we attempt to construct in the appropriate model format, based on our understanding of the observed physical data and on the associated statistical mechanism, analytically represented by suitable probability measures. Since its inception in the late '30's of the last century, and in particular subsequent to World War II, SCT has grown into a major field of study. As we have noted above, SCT is applicable to all branches of science. The latter itself is inherently and ultimately probabilistic at all levels. Moreover, in the natural world there is always a random background "noise" as well as an inherent a priori uncertainty in the presentation of deterministic observations, i.e. those which are specifically obtained, a posteriori. The purpose of the book is to introduce Non-

**Gaussian**statistical communication theory and demonstrate how the theory improves probabilistic model. The book was originally planed to include 24 chapters as seen in the table of preface. Dr. Middleton completed first 10 chapters prior to his passing in 2008. Bibliography which represents remaining chapters are put together by the author's close colleagues; Drs. Vincent Poor, Leon Cohen and John Anderson. email pressbooks@ieee.org to request Ch.10Category: Technology. ISBN: 9780470948477

### Large Deviations for **Gaussian** Queues

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In recent years the significance of

**Gaussian**processes to communication networks has grown considerably. The inherent flexibility of the**Gaussian**traffic model enables the analysis, in a single mathematical framework, of systems with both long-range and short-range dependent input streams. Large Deviations for**Gaussian**Queues demonstrates how the**Gaussian**traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. The text provides a general introduction to**Gaussian**queues, and surveys recent research into the modelling of communications networks. Coverage includes: Discussion of the theoretical concepts and practical aspects related to**Gaussian**traffic models. Analysis of recent research asymptotic results for**Gaussian**queues, both in the large-buffer and many-sources regime. An emphasis on rare-event analysis, relying on a variety of asymptotic techniques. Examination of single-node FIFO queuing systems, as well as queues operating under more complex scheduling disciplines, and queuing networks. A set of illustrative examples that directly relate to important practical problems in communication networking. A large collection of instructive exercises and accompanying solutions. Large Deviations for**Gaussian**Queues assumes minimal prior knowledge. It is ideally suited for postgraduate students in applied probability, operations research, computer science and electrical engineering. The book’s self-contained style makes it perfect for practitioners in the communications networking industry and for researchers in related areas.Category: Technology. ISBN: 9780470015230

**Gaussian** Basis Sets for Molecular Calculations

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Physical Sciences Data, Volume 16:

**Gaussian**Basis Sets for Molecular Calculations provides information pertinent to the**Gaussian**basis sets, with emphasis on lithium, radon, and important ions. This book discusses the polarization functions prepared for lithium through radon for further improvement of the basis sets. Organized into three chapters, this volume begins with an overview of the basis set for the most stable negative and positive ions. This text then explores the total atomic energies given by the basis sets. Other chapters consider the distinction between diffuse functions and polarization function. This book presents as well the exponents of polarization function. The final chapter deals with the**Gaussian**basis sets. This book is a valuable resource for chemists, scientists, and research workers.Category: Science. ISBN: 9780444422545

**Gaussian** Process Regression Analysis for Functional Data

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**Gaussian**Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a

**Gaussian**process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of

**Gaussian**process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of

**Gaussian**process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-

**Gaussian**data. Many flexible models based on

**Gaussian**processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these

**Gaussian**process regression models in the analysis of functional data. Some MATLAB and C codes are available on the first author's website.

Category: Science. ISBN: 9781439837733

### Theory and Applications of **Gaussian** Quadrature Methods

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**Gaussian**quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of

**Gaussian**quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions and examine the analytical framework of

**Gaussian**quadrature. We discuss

**Gaussian**quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of

**Gaussian**quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided.Table of Contents: Introduction / Approximating with Polynomials and Related Functions /

**Gaussian**Quadrature / Applications / Links to Mathematical Software

Category: Technology. ISBN: 9781608457533

### Probability Distributions Involving **Gaussian** Random Variables

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This handbook brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians.

Category: Technology. ISBN: 9780387346571

### Non-**Gaussian** Merton-Black-Scholes Theory

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This book introduces an analytically tractable and computationally effective class of non-

**Gaussian**models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton–Black–Scholes approach, which the authors call the Merton–Black–Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-**Gaussian**situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further. Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics. Sample Chapter(s). Chapter 1.1: The**Gaussian**Merton-Black-Scholes theory (298 KB). Chapter 1.2: Regular Lévy Processes of Exponential type (271 KB). Chapter 1.3: Pricing of contingent claims (247 KB). Chapter 1.4: The Generalized Black-Scholes equation (207 KB). Chapter 1.5: Analytical methods used in the book (204 KB). Chapter 1.6: An overview of the results covered in the book (206 KB). Chapter 1.7: Commentary (112 KB). Contents: Lévy Processes; Regular Lévy Processes of Exponential Type in 1D; Pricing and Hedging of Contingent Claims of European Type; Perpetual American Options; American Options: Finite Time Horizon; First-Touch Digitals; Barrier Options; Multi-Asset Contracts; Investment Under Uncertainty and Capital Accumulation; Endogenous Default and Pricing of the Corporate Debt; Fast Pricing of European Options; Discrete Time Models; Feller Processes of Normal Inverse**Gaussian**Type; Pseudodifferential Operators with Constant Symbols; Elements of Calculus of Pseudodifferential Operators. Readership: Graduate students, researchers and academics in economics, mathematical finance, banking & finance/accounting; and financial engineers.Category: Business. ISBN: 9789810249441

### Markov Processes, **Gaussian** Processes, and Local Times

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A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.

Category: Technology. ISBN: 9780521863001

### Financial Modeling Under Non-**Gaussian** Distributions

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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

### VaR Methodology for Non-**Gaussian** Finance

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With the impact of the recent financial crises, more attention must be given to new models in finance rejecting “Black-Scholes-Samuelson” assumptions leading to what is called non-

**Gaussian**finance. With the growing importance of Solvency II, Basel II and III regulatory rules for insurance companies and banks, value at risk (VaR) – one of the most popular risk indicator techniques plays a fundamental role in defining appropriate levels of equities. The aim of this book is to show how new VaR techniques can be built more appropriately for a crisis situation. VaR methodology for non-**Gaussian**finance looks at the importance of VaR in standard international rules for banks and insurance companies; gives the first non-**Gaussian**extensions of VaR and applies several basic statistical theories to extend classical results of VaR techniques such as the NP approximation, the Cornish-Fisher approximation, extreme and a Pareto distribution. Several non-**Gaussian**models using Copula methodology, Lévy processes along with particular attention to models with jumps such as the Merton model are presented; as are the consideration of time homogeneous and non-homogeneous Markov and semi-Markov processes and for each of these models. Contents 1. Use of Value-at-Risk (VaR) Techniques for Solvency II, Basel II and III. 2. Classical Value-at-Risk (VaR) Methods. 3. VaR Extensions from**Gaussian**Finance to Non-**Gaussian**Finance. 4. New VaR Methods of Non-**Gaussian**Finance. 5. Non-**Gaussian**Finance: Semi-Markov Models. About the Authors Marine Habart-Corlosquet is a Qualified and Certified Actuary at BNP Paribas Cardif, Paris, France. She is co-director of EURIA (Euro-Institut d’Actuariat, University of West Brittany, Brest, France), and associate researcher at Telecom Bretagne (Brest, France) as well as a board member of the French Institute of Actuaries. She teaches at EURIA, Telecom Bretagne and Ecole Centrale Paris (France). Her main research interests are pandemics, Solvency II internal models and ALM issues for insurance companies. Jacques Janssen is now Honorary Professor at the Solvay Business School (ULB) in Brussels, Belgium, having previously taught at EURIA (Euro-Institut d’Actuariat, University of West Brittany, Brest, France) and Telecom Bretagne (Brest, France) as well as being a director of Jacan Insurance and Finance Services, a consultancy and training company. Raimondo Manca is Professor of mathematical methods applied to economics, finance and actuarial science at University of Roma “La Sapienza” in Italy. He is associate editor for the journal Methodology and Computing in Applied Probability. His main research interests are multidimensional linear algebra, computational probability, application of stochastic processes to economics, finance and insurance and simulation models.Category: Business. ISBN: 9781848214644