### Stable Non-**Gaussian** Self-Similar Processes with Stationary Increments

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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

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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

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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

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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

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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

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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

### Bipartite Graphs and their Applications

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

**Gaussian**random variables.Category: Mathematics. ISBN: 9780521593458

### Quantum Information Ii

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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

### The Oxford Handbook of Credit Derivatives

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Provides a timely discussion of the mathematical modelling that underpins both credit derivatives and securitisation. It covers statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk,

**Gaussian**and non-**Gaussian**modelling, and securitisation.Category: Business. ISBN: 9780199546787

### The Oxford Handbook of Credit Derivatives

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Provides a timely discussion of the mathematical modelling that underpins both credit derivatives and securitisation. It covers statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk,

**Gaussian**and non-**Gaussian**modelling, and securitisation.Category: Business. ISBN: 9780199546787