Probabilistic Techniques In Analysis
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Probabilistic Techniques In Analysis
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Author : Richard F. Bass
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-12-16
Probabilistic Techniques In Analysis written by Richard F. Bass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-16 with Mathematics categories.
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.
Probabilistic And Stochastic Methods In Analysis With Applications
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Author : J.S. Byrnes
language : en
Publisher: Springer
Release Date : 2012-10-13
Probabilistic And Stochastic Methods In Analysis With Applications written by J.S. Byrnes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-13 with Mathematics categories.
Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.
Probability And Computing
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Author : Michael Mitzenmacher
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-31
Probability And Computing written by Michael Mitzenmacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-31 with Computers categories.
Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
Probability And Computing
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Author : Michael Mitzenmacher
language : en
Publisher: Cambridge University Press
Release Date : 2017-07-03
Probability And Computing written by Michael Mitzenmacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-03 with Computers categories.
This greatly expanded new edition offers a comprehensive introduction to randomization and probabilistic techniques in modern computer science.
Probabilistic Methods In Geotechnical Engineering
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Author : D. V. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Probabilistic Methods In Geotechnical Engineering written by D. V. Griffiths and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Science categories.
Learn to use probabilistic techniques to solve problems in geotechnical engineering. The book reviews the statistical theories needed to develop the methodologies and interpret the results. Next, the authors explore probabilistic methods of analysis, such as the first order second moment method, the point estimate method, and random set theory. Examples and case histories guide you step by step in applying the techniques to particular problems.
Mathematical Techniques For Analyzing Concurrent And Probabilistic Systems
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Author : J. J. M. M. Rutten
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Mathematical Techniques For Analyzing Concurrent And Probabilistic Systems written by J. J. M. M. Rutten and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Discrete-time systems categories.
The book consists of two sets of lecture notes devoted to slightly different methods of analysis of concurrent and probabilistic computational systems. The first set of lectures develops a calculus of streams (a generalization of the set of natural numbers) based on the coinduction principle coming from the theory of coalgebras. It is now well understood that the interplay between algebra (for describing structure) and coalgebra (for describing dynamics) is crucial for understandingconcurrent systems. There is a striking analogy between streams and formula calculus reminiscent of those appearing in quantum calculus. These lecture notes will appeal to anyone working in concurrency theory but also to algebraists and logicians. The other set of lecture notes focuses on methodsfor automatically verifying probabilistic systems using techniques of model checking. The unique aspect of these lectures is the coverage of both theory and practice. The authors have been responsible for one of the most successful experimental systems for probabilistic model checking. These lecture notes are of interest to software engineers, real-time programmers, researchers in machine learning and numerical analysts who may well be interested to see how standard numerical techniques areused in a novel context. Both sets of lectures are expository and suitable for graduate courses in theoretical computer science and for research mathematicians interested in design and analysis of concurrent and probabilistic computational systems.
Probability And Computing
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Author : Michael Mitzenmacher
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-31
Probability And Computing written by Michael Mitzenmacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-31 with Computers categories.
Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
Lectures On Stochastic Analysis Diffusion Theory
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Author : Daniel W. Stroock
language : en
Publisher:
Release Date : 2014-05-14
Lectures On Stochastic Analysis Diffusion Theory written by Daniel W. Stroock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.
The Probabilistic Method
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Author : Noga Alon
language : en
Publisher: John Wiley & Sons
Release Date : 2015-11-02
The Probabilistic Method written by Noga Alon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-02 with Mathematics categories.
Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
Probabilistic Techniques In Exposure Assessment
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Author : Alison C. Cullen
language : en
Publisher: Springer Science & Business
Release Date : 1999-07-31
Probabilistic Techniques In Exposure Assessment written by Alison C. Cullen and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-31 with Medical categories.
In this text, experts provide a complete sourcebook on methods for addressing variability and uncertainty in exposure analysis.