### Analysis on **Gaussian** Spaces

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Analysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the

**Gaussian**measure, which has been unified under the terminology of "abstract Wiener space". Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the**Gaussian**space itself such as the Brunn–Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the**Gaussian**space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer theory are given in details. This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood–Paley–Stein–Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.Category: Mathematics. ISBN: 9789813142176

**Gaussian** Random Fields

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Far from being a melting pot, multi-racial Singapore prides itself on the richness of its ethnic communities and cultures. This volume provides an updated account of the heterogeneity within each of the main communities — the Chinese, Malay, Indian, Eurasian and Others. It also documents the ethnic cultures of these communities by discussing their histories, celebrations, cultural symbols, life cycle rituals, cultural icons and attempts to preserve culture. While chapters are written by scholars drawing insight from a variety of sources ranging from academic publications to discussions with community experts, it is written in an accessible way. This volume seeks to increase intercultural understanding through presenting ample insights into the cultural beliefs and practices of the different ethnic communities. While this book is about diversity, a closer examination of the peoples and cultures of Singapore demonstrates the many similarities communities share in this Singaporean space.

Category: General. ISBN: 9789810205058

### The Inverse **Gaussian** Distribution

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This book is written in the hope that it will serve as a companion volume to my first monograph. The first monograph was largely devoted to the probabilistic aspects of the inverse

**Gaussian**law and therefore ignored the statistical issues and related data analyses. Ever since the appearance of the book by Chhikara and Folks, a considerable number of publications in both theory and applications of the inverse**Gaussian**law have emerged thereby justifying the need for a comprehensive treatment of the issues involved. This book is divided into two sections and fills up the gap updating the material found in the book of Chhikara and Folks. Part I contains seven chapters and covers distribution theory, estimation, significance tests, goodness-of-fit, sequential analysis and compound laws and mixtures. The first part forms the backbone of the theory and wherever possible I have provided illustrative examples for easy assimilation of the theory. The second part is devoted to a wide range of applications from various disciplines. The applied statistician will find numerous instances of examples which pertain to a first passage time situation. It is indeed remarkable that in the fields of life testing, ecology, entomology, health sciences, traffic intensity and management science the inverse**Gaussian**law plays a dominant role. Real life examples from actuarial science and ecology came to my attention after this project was completed and I found it impossible to include them.Category: Mathematics. ISBN: 9780387986180

**Gaussian** Hilbert Spaces

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This book treats the fundamental mathematical properties that hold for a family of

**Gaussian**random variables.Category: Mathematics. ISBN: 9780521561280

### Sums and **Gaussian** Vectors

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Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble

**Gaussian**laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.Category: Science. ISBN: 9783540603115

**Gaussian** Processes on Trees

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This book presents recent advances in branching Brownian motion from the perspective of extreme value theory and statistical physics, for graduates.

Category: Science. ISBN: 9781107160491

### Generalized **Gaussian** Error Calculus

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This book addresses a rigorous, complete and self-consistent revision of the

**Gaussian**error calculus. It integrates mathematics and its applications to physical measurements, and serves as a text for graduate students and a reference for researchers.Category: Technology. ISBN: 9783642033049

### Lectures on **Gaussian** Processes

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**Gaussian**processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of

**Gaussian**processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such assmall deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.

Category: Mathematics. ISBN: 9783642249389

**Gaussian** Markov Random Fields

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**Gaussian**Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.

Category: Science. ISBN: 9781584884323

### The **Gaussian** Approximation Potential

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The framework of

**Gaussian**Approximation Potentials developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The method has already been successfully applied to semiconductors and metals.Category: Science. ISBN: 9783642140662