Analysis and Probability Book

Analysis and Probability


  • Author : Aurel Spataru
  • Publisher : Newnes
  • Release Date : 2013-01-12
  • Genre: Mathematics
  • Pages : 404
  • ISBN 10 : 9780124017276

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Analysis and Probability Excerpt :

Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodology and fundamental results of probability theory. Exercises are included throughout the text, not just at the end, to teach each concept fully as it is explained, including presentations of interesting extensions of the theory. The complete and detailed nature of the book makes it ideal as a reference book or for self-study in probability and related fields. Covers a wide range of subjects including f-expansions, Fuk-Nagaev inequalities and Markov triples. Provides multiple clearly worked exercises with complete proofs. Guides readers through examples so they can understand and write research papers independently.

Real Analysis and Probability Book
Score: 5
From 3 Ratings

Real Analysis and Probability


  • Author : R. M. Dudley
  • Publisher : Cambridge University Press
  • Release Date : 2002-10-14
  • Genre: Mathematics
  • Pages : 570
  • ISBN 10 : 0521007542

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Real Analysis and Probability Excerpt :

This classic text offers a clear exposition of modern probability theory.

Analysis and Probability Book
Score: 5
From 1 Ratings

Analysis and Probability


  • Author : Palle E. T. Jorgensen
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-10-17
  • Genre: Mathematics
  • Pages : 280
  • ISBN 10 : 9780387330822

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Analysis and Probability Excerpt :

Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

Functional Analysis for Probability and Stochastic Processes Book

Functional Analysis for Probability and Stochastic Processes


  • Author : Adam Bobrowski
  • Publisher : Cambridge University Press
  • Release Date : 2005-08-11
  • Genre: Mathematics
  • Pages : 416
  • ISBN 10 : 0521831660

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Functional Analysis for Probability and Stochastic Processes Excerpt :

This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.

Real Analysis and Probability Book

Real Analysis and Probability


  • Author : Robert B. Ash
  • Publisher : Academic Press
  • Release Date : 2014-07-03
  • Genre: Mathematics
  • Pages : 494
  • ISBN 10 : 9781483191423

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Real Analysis and Probability Excerpt :

Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory. Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of various applications of the basic integration theory. The reader is then introduced to functional analysis, with emphasis on structures that can be defined on vector spaces. Subsequent chapters focus on the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also examined, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, paying particular attention to the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.

Real Analysis and Probability Book
Score: 2
From 1 Ratings

Real Analysis and Probability


  • Author : R. M. Dudley
  • Publisher : CRC Press
  • Release Date : 2018-02-01
  • Genre: Mathematics
  • Pages : 405
  • ISBN 10 : 9781351093095

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Real Analysis and Probability Excerpt :

Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.

Inequalities in Analysis and Probability Book

Inequalities in Analysis and Probability


  • Author : Odile Pons
  • Publisher : World Scientific
  • Release Date : 2016-11-03
  • Genre: Mathematics
  • Pages : 308
  • ISBN 10 : 9789813144002

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Inequalities in Analysis and Probability Excerpt :

The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane. This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.

Geometry  Analysis and Probability Book

Geometry Analysis and Probability


  • Author : Jean-Benoît Bost
  • Publisher : Birkhäuser
  • Release Date : 2017-04-26
  • Genre: Mathematics
  • Pages : 361
  • ISBN 10 : 9783319496382

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Geometry Analysis and Probability Excerpt :

This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

Harmonic Analysis and the Theory of Probability Book

Harmonic Analysis and the Theory of Probability


  • Author : Salomon Bochner
  • Publisher : Courier Corporation
  • Release Date : 2013-11-07
  • Genre: Mathematics
  • Pages : 192
  • ISBN 10 : 9780486154800

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Harmonic Analysis and the Theory of Probability Excerpt :

Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.

Probability Methods for Cost Uncertainty Analysis Book

Probability Methods for Cost Uncertainty Analysis


  • Author : Paul R. Garvey
  • Publisher : CRC Press
  • Release Date : 2016-01-06
  • Genre: Mathematics
  • Pages : 524
  • ISBN 10 : 9781482219760

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Probability Methods for Cost Uncertainty Analysis Excerpt :

Probability Methods for Cost Uncertainty Analysis: A Systems Engineering Perspective, Second Edition gives you a thorough grounding in the analytical methods needed for modeling and measuring uncertainty in the cost of engineering systems. This includes the treatment of correlation between the cost of system elements, how to present the analysis to

Fourier Analysis in Probability Theory Book

Fourier Analysis in Probability Theory


  • Author : Tatsuo Kawata
  • Publisher : Academic Press
  • Release Date : 2014-06-17
  • Genre: Mathematics
  • Pages : 680
  • ISBN 10 : 9781483218526

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Fourier Analysis in Probability Theory Excerpt :

Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.

Quantum Probability and Spectral Analysis of Graphs Book

Quantum Probability and Spectral Analysis of Graphs


  • Author : Akihito Hora
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-07-05
  • Genre: Science
  • Pages : 371
  • ISBN 10 : 9783540488637

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Quantum Probability and Spectral Analysis of Graphs Excerpt :

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Probabilistic Techniques in Analysis Book
Score: 3
From 1 Ratings

Probabilistic Techniques in Analysis


  • Author : Richard F. Bass
  • Publisher : Springer Science & Business Media
  • Release Date : 1994-12-16
  • Genre: Mathematics
  • Pages : 408
  • ISBN 10 : 9780387943879

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Probabilistic Techniques in Analysis Excerpt :

In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.

Fractals in Probability and Analysis Book

Fractals in Probability and Analysis


  • Author : Christopher J. Bishop
  • Publisher : Cambridge University Press
  • Release Date : 2017
  • Genre: Mathematics
  • Pages : 415
  • ISBN 10 : 9781107134119

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Fractals in Probability and Analysis Excerpt :

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Probability Book

Probability


  • Author : Guy Lebanon
  • Publisher : Unknown
  • Release Date : 2012-10-09
  • Genre: Machine learning
  • Pages : 346
  • ISBN 10 : 1479344761

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Probability Excerpt :

Introduction to probability theory with an emphasis on the multivariate case. Includes random vectors, random processes, Markov chains, limit theorems, and related mathematics such as metric spaces, measure theory, and integration.