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Lectures on Gaussian Processes

Posted By: AvaxGenius
Lectures on Gaussian Processes

Lectures on Gaussian Processes by Mikhail Lifshits
English | PDF (True) | 2012 | 129 Pages | ISBN : 3642249388 | 2.7 MB

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 as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.​

Failure Rate Modelling for Reliability and Risk

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Failure Rate Modelling for Reliability and Risk

Failure Rate Modelling for Reliability and Risk by Maxim Finkelstein
English | PDF | 2008 | 297 Pages | ISBN : 1848009852 | 4.3 MB

“Failure Rate Modeling for Reliability and Risk” focuses on reliability theory, and to the failure rate (hazard rate, force of mortality) modeling and its generalizations to systems operating in a random environment and to repairable systems. The failure rate is one of the crucial probabilistic characteristics for a number of disciplines; including reliability, survival analysis, risk analysis and demography. The book presents a systematic study of the failure rate and related indices, and covers a number of important applications where the failure rate plays the major role. Applications in engineering systems are studied, together with some actuarial, biological and demographic examples. The book provides a survey of this broad and interdisciplinary subject which will be invaluable to researchers and advanced students in reliability engineering and applied statistics, as well as to demographers, econometricians, actuaries and many other mathematically oriented researchers.

Modeling with Itô Stochastic Differential Equations (Repost)

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Modeling with Itô Stochastic Differential Equations (Repost)

Modeling with Itô Stochastic Differential Equations by E. Allen
English | PDF | 2007 | 238 Pages | ISBN : 1402059523 | 1.6 MB

Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained.

The Random-Cluster Model

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The Random-Cluster Model

The Random-Cluster Model by Geoffrey R. Grimmett
English | PDF | 2006 | 390 Pages | ISBN : 3540328904 | 4.3 MB

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.

Numerical Methods in Sensitivity Analysis and Shape Optimization

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Numerical Methods in Sensitivity Analysis and Shape Optimization

Numerical Methods in Sensitivity Analysis and Shape Optimization by Emmanuel Laporte , Patrick Tallec
English | PDF | 2003 | 202 Pages | ISBN : 0817643222 | 12.3 MB

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers.

Validation of Stochastic Systems: A Guide to Current Research

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Validation of Stochastic Systems: A Guide to Current Research

Validation of Stochastic Systems: A Guide to Current Research by Christel Baier, Boudewijn R. Haverkort, Holger Hermanns, Joost-Pieter Katoen, Markus Siegle
English | PDF | 2004 | 473 Pages | ISBN : 3540222650 | 4 MB

This tutorial volume presents a coherent and well-balanced introduction to the validation of stochastic systems; it is based on a GI/Dagstuhl research seminar. Supervised by the seminar organizers and volume editors, established researchers in the area as well as graduate students put together a collection of articles competently covering all relevant issues in the area. The lectures are organized in topical sections on: modeling stochastic systems, model checking of stochastic systems, representing large state spaces, deductive verification of stochastic systems.

Logic and Complexity

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Logic and Complexity

Logic and Complexity by Richard Lassaigne , Michel Rougemont
English | PDF | 2004 | 361 Pages | ISBN : 1852335653 | 30.2 MB

Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.

COMPSTAT 2004 - Proceedings in Computational Statistics

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COMPSTAT 2004 - Proceedings in Computational Statistics

COMPSTAT 2004 - Proceedings in Computational Statistics: 16th Symposium Held in Prague, Czech Republic, 2004 by Jaromir Antoch
English | PDF | 2004 | 578 Pages | ISBN : 3790815543 | 67.3 MB

Statistical computing provides the link between statistical theory and applied statistics. As at previous COMPSTAT volumes, the content of the book covers all aspects of this link, from the development and implementation of new statistical ideas to user experiences and software evaluation. The proceedings should appeal to anyone working in statistics and using computers, whether in universities, industrial companies, government agencies, research institutes or as software developers.

The Cramér–Lundberg Model and Its Variants: A Queueing Perspective

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The Cramér–Lundberg Model and Its Variants: A Queueing Perspective

The Cramér–Lundberg Model and Its Variants: A Queueing Perspective by Michel Mandjes , Onno Boxma
English | PDF EPUB (True) | 2023 | 252 Pages | ISBN : 3031391047 | 23.4 MB

This book offers a comprehensive examination of the Cramér–Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants.

Diffusion Under Confinement: A Journey Through Counterintuition

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Diffusion Under Confinement: A Journey Through Counterintuition

Diffusion Under Confinement: A Journey Through Counterintuition by Leonardo Dagdug , Jason Peña , Ivan Pompa-García
English | PDF EPUB (True) | 2024 | 759 Pages | ISBN : 3031464745 | 100.8 MB

This book offers the reader a journey through the counterintuitive nature of Brownian motion under confinement. Diffusion is a universal phenomenon that controls a wide range of physical, chemical, and biological processes. The transport of spatially-constrained molecules and small particles is ubiquitous in nature and technology and plays an essential role in different processes. Understanding the physics of diffusion under conditions of confinement is essential for a number of biological phenomena and potential technological applications in micro- and nanofluidics, among others.

Stochastic Approximation: A Dynamical Systems Viewpoint

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Stochastic Approximation: A Dynamical Systems Viewpoint

Stochastic Approximation: A Dynamical Systems Viewpoint by Vivek S. Borkar
English | PDF EPUB (True) | 2024 | 280 Pages | ISBN : 9819982766 | 28.7 MB

This book serves as an advanced text for a graduate course on stochastic algorithms for the students of probability and statistics, engineering, economics and machine learning. This second edition gives a comprehensive treatment of stochastic approximation algorithms based on the ordinary differential equation (ODE) approach which analyses the algorithm in terms of a limiting ODE. It has a streamlined treatment of the classical convergence analysis and includes several recent developments such as concentration bounds, avoidance of traps, stability tests, distributed and asynchronous schemes, multiple time scales, general noise models, etc., and a category-wise exposition of many important applications. It is also a useful reference for researchers and practitioners in the field.

Real and Stochastic Analysis: New Perspectives

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Real and Stochastic Analysis: New Perspectives

Real and Stochastic Analysis: New Perspectives by M. M. Rao
English | PDF | 2004 | 411 Pages | ISBN : 081764332X | 45.9 MB

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov­ ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil­ ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

Stochastic Processes and Related Topics

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Stochastic Processes and Related Topics

Stochastic Processes and Related Topics: In Memory of Stamatis Cambanis 1943–1995 by Ioannis Karatzas, Balram S. Rajput, Murad S. Taqqu
English | PDF | 1998 | 391 Pages | ISBN : 0817639985 | 30.8 MB

In the last twenty years extensive research has been devoted to a better understanding of the stable and other closely related infinitely divisible mod­ els. Stamatis Cambanis, a distinguished educator and researcher, played a special leadership role in the development of these research efforts, particu­ larly related to stable processes from the early seventies until his untimely death in April '95. This commemorative volume consists of a collection of research articles devoted to reviewing the state of the art of this and other rapidly developing research and to explore new directions of research in these fields.

Stochastic Analysis and Mathematical Physics

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Stochastic Analysis and Mathematical Physics

Stochastic Analysis and Mathematical Physics: ANESTOC ’98 Proceedings of the Third International Workshop by Rolando Rebolledo
English | PDF | 2000 | 168 Pages | ISBN : 0817641858 | 11.1 MB

The seminar on Stochastic Analysis and Mathematical Physics started in 1984 at the Catholic University of Chile in Santiago and has been an on­ going research activity. Since 1995, the group has organized international workshops as a way of promoting a broader dialogue among experts in the areas of classical and quantum stochastic analysis, mathematical physics and physics. This volume, consisting primarily of contributions to the Third Inter­ national Workshop on Stochastic Analysis and Mathematical Physics (in Spanish ANESTOC), held in Santiago, Chile, in October 1998, focuses on an analysis of quantum dynamics and related problems in probability the­ ory. Various articles investigate quantum dynamical semigroups and new results on q-deformed oscillator algebras, while others examine the appli­ cation of classical stochastic processes in quantum modeling. As in previous workshops, the topic of quantum flows and semigroups occupied an important place.

Stochastic Analysis and Mathematical Physics II: 4th International ANESTOC Workshop in Santiago, Chile

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Stochastic Analysis and Mathematical Physics II: 4th International ANESTOC Workshop in Santiago, Chile

Stochastic Analysis and Mathematical Physics II: 4th International ANESTOC Workshop in Santiago, Chile by Rolando Rebolledo
English | PDF | 2003 | 172 Pages | ISBN : 3764369973 | 12.7 MB

The seminar on Stochastic Analysis and Mathematical Physics of the Ca­ tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro­ moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physics, and physics. This volume collects most of the contributions to the Fourth Interna­ tional Workshop on Stochastic Analysis and Mathematical Physics (whose Spanish abbreviation is "ANESTOC"; in English, "STAMP"), held in San­ tiago, Chile, from January 5 to 11, 2000. The workshop style stimulated a vivid exchange of ideas which finally led to a number of written con­ tributions which I am glad to introduce here. However, we are currently submitted to a sort of invasion of proceedings books, and we do not want to increase our own shelves with a new one of the like. On the other hand, the editors of conference proceedings have to use different exhausting and com­ pulsive strategies to persuade authors to write and provide texts in time, a task which terrifies us. As a result, this volume is aimed at smoothly start­ ing a new kind of publication. What we would like to have is a collection of books organized like our seminar.