### Simulation of Stochastic Processes with Given Accuracy and Reliability

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Simulation has now become an integral part of research and development across many fields of study. Despite the large amounts of literature in the field of simulation and modeling, one recurring problem is the issue of accuracy and confidence level of constructed models. By outlining the new approaches and modern methods of simulation of stochastic processes, this book provides methods and tools in measuring accuracy and reliability in functional spaces. The authors explore analysis of the theory of Sub-

**Gaussian**(including**Gaussian**one) and Square**Gaussian**random variables and processes and Cox processes. Methods of simulation of stochastic processes and fields with given accuracy and reliability in some Banach spaces are also considered. Provides an analysis of the theory of Sub-**Gaussian**(including**Gaussian**one) and Square**Gaussian**random variables and processes Contains information on the study of the issue of accuracy and confidence level of constructed models not found in other books on the topic Provides methods and tools in measuring accuracy and reliability in functional spacesCategory: Mathematics. ISBN: 9781785482175

### Bayesian Estimation and Tracking

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A practical approach to estimating and tracking dynamic systems in real-worl applications Much of the literature on performing estimation for non-

**Gaussian**systems is short on practical methodology, while**Gaussian**methods often lack a cohesive derivation. Bayesian Estimation and Tracking addresses the gap in the field on both accounts, providing readers with a comprehensive overview of methods for estimating both linear and nonlinear dynamic systems driven by**Gaussian**and non-**Gaussian**noices. Featuring a unified approach to Bayesian estimation and tracking, the book emphasizes the derivation of all tracking algorithms within a Bayesian framework and describes effective numerical methods for evaluating density-weighted integrals, including linear and nonlinear Kalman filters for**Gaussian**-weighted integrals and particle filters for non-**Gaussian**cases. The author first emphasizes detailed derivations from first principles of eeach estimation method and goes on to use illustrative and detailed step-by-step instructions for each method that makes coding of the tracking filter simple and easy to understand. Case studies are employed to showcase applications of the discussed topics. In addition, the book supplies block diagrams for each algorithm, allowing readers to develop their own MATLAB® toolbox of estimation methods. Bayesian Estimation and Tracking is an excellent book for courses on estimation and tracking methods at the graduate level. The book also serves as a valuable reference for research scientists, mathematicians, and engineers seeking a deeper understanding of the topics.Category: Technology. ISBN: 9780470621707

### Nonlinear Signal Processing

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Nonlinear Signal Processing: A Statistical Approach focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non-

**Gaussian**, rather than**Gaussian**, processes. Notably, by concentrating on just two non-**Gaussian**models, a large set of tools is developed that encompass a large portion of the nonlinear signal processing tools proposed in the literature over the past several decades. Key features include: * Numerous problems at the end of each chapter to aid development and understanding * Examples and case studies provided throughout the book in a wide range of applications bring the text to life and place the theory into context * A set of 60+ MATLAB software m-files allowing the reader to quickly design and apply any of the nonlinear signal processing algorithms described in the book to an application of interest is available on the accompanying FTP site.Category: Technology. ISBN: 9780471676249

### 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

### Statistical Mechanics for Athermal Fluctuation

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The author investigates athermal fluctuation from the viewpoints of statistical mechanics in this thesis. Stochastic methods are theoretically very powerful in describing fluctuation of thermodynamic quantities in small systems on the level of a single trajectory and have been recently developed on the basis of stochastic thermodynamics. This thesis proposes, for the first time, a systematic framework to describe athermal fluctuation, developing stochastic thermodynamics for non-

**Gaussian**processes, while thermal fluctuations are mainly addressed from the viewpoint of**Gaussian**stochastic processes in most of the conventional studies. First, the book provides an elementary introduction to the stochastic processes and stochastic thermodynamics. The author derives a Langevin-like equation with non-**Gaussian**noise as a minimal stochastic model for athermal systems, and its analytical solution by developing systematic expansions is shown as the main result. Furthermore, the a uthor shows a thermodynamic framework for such non-**Gaussian**fluctuations, and studies some thermodynamics phenomena, i.e. heat conduction and energy pumping, which shows distinct characteristics from conventional thermodynamics. The theory introduced in the book would be a systematic foundation to describe dynamics of athermal fluctuation quantitatively and to analyze their thermodynamic properties on the basis of stochastic methods.Category: Science. ISBN: 9789811063305

### 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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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