### Probabilistic Analysis and Related Topics

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Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of

**Gaussian**measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and**Gaussian**processes, equivalence and singularity of**Gaussian**processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.Category: Mathematics. ISBN: 9780120956012

### Quantum Continuous Variables

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Quantum Continuous Variables introduces the theory of continuous variable quantum systems, from its foundations based on the framework of

**Gaussian**states to modern developments, including its applications to quantum information and forthcoming quantum technologies. This new book addresses the theory of**Gaussian**states, operations, and dynamics in great depth and breadth, through a novel approach that embraces both the Hilbert space and phase descriptions. The volume includes coverage of entanglement theory and quantum information protocols, and their connection with relevant experimental set-ups. General techniques for non-**Gaussian**manipulations also emerge as the treatment unfolds, and are demonstrated with specific case studies. This book will be of interest to graduate students looking to familiarise themselves with the field, in addition to experienced researchers eager to enhance their understanding of its theoretical methods. It will also appeal to experimentalists searching for a rigorous but accessible treatment of the theory in the area.Category: Computers. ISBN: 9781482246346

### Issues in the Use of Neural Networks in Information Retrieval

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This book highlights the ability of neural networks (NNs) to be excellent pattern matchers and their importance in information retrieval (IR), which is based on index term matching. The book defines a new NN-based method for learning image similarity and describes how to use fuzzy

**Gaussian**neural networks to predict personality. It introduces the fuzzy Clifford**Gaussian**network, and two concurrent neural models: (1) concurrent fuzzy nonlinear perceptron modules, and (2) concurrent fuzzy**Gaussian**neural network modules. Furthermore, it explains the design of a new model of fuzzy nonlinear perceptron based on alpha level sets and describes a recurrent fuzzy neural network model with a learning algorithm based on the improved particle swarm optimization method.Category: Computers. ISBN: 9783319438702

### Mixture Model-Based Classification

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Mixture Model-Based Classification is the first monograph devoted to mixture model-based approaches to clustering and classification. This is both a book for established researchers and newcomers to the field. A history of mixture models as a tool for classification is provided and

**Gaussian**mixtures are considered extensively, including mixtures of factor analyzers and other approaches for high-dimensional data. Non-**Gaussian**mixtures are considered, from mixtures with components that parameterize skewness and/or concentration, right up to mixtures of multiple scaled distributions. Several other important topics are considered, including mixture approaches for clustering and classification of longitudinal data as well as discussion about how to define a cluster.Category: Mathematics. ISBN: 9781482225662

### Missing Data Methods

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Contains 16 chapters authored by specialists in the field, covering topics such as: Missing-Data Imputation in Nonstationary Panel Data Models; Markov Switching Models in Empirical Finance; Bayesian Analysis of Multivariate Sample Selection Models Using

**Gaussian**Copulas; and, Consistent Estimation and Orthogonality.Category: Business. ISBN: 9781780525242

### Stochastic Analysis

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This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a

**Gaussian**probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.Category: Mathematics. ISBN: 9783540570240

### Missing Data Methods

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Part of the "Advances in Econometrics" series, this title contains chapters covering topics such as: Missing-Data Imputation in Nonstationary Panel Data Models; Markov Switching Models in Empirical Finance; Bayesian Analysis of Multivariate Sample Selection Models Using

**Gaussian**Copulas; and, Consistent Estimation and Orthogonality.Category: Business. ISBN: 9781780525266

### Time Series Analysis by State Space Methods

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This new edition updates Durbin & Koopman's important text on the state space approach to time series analysis providing a more comprehensive treatment, including the filtering of nonlinear and non-

**Gaussian**series. The book provides an excellent source for the development of practical courses on time series analysis.Category: Business. ISBN: 9780199641178

### Handbook of Heavy Tailed Distributions in Finance

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The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series. This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non-

**Gaussian**assumptions, as well as the applications of the stable and other non -**Gaussian**models in finance and risk management.Category: Business. ISBN: 9780444508966

### White Noise Calculus and Fock Space

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White Noise Calculus is a distribution theory on

**Gaussian**space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on**Gaussian**space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.Category: Science. ISBN: 9783540579854