Multidimensional Stochastic Processes As Rough Paths
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Multidimensional Stochastic Processes As Rough Paths
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Author : Peter K. Friz
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-04
Multidimensional Stochastic Processes As Rough Paths written by Peter K. Friz 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 2010-02-04 with Mathematics categories.
Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.
Multidimensional Stochastic Processes As Rough Paths
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Author : Peter K. Friz
language : en
Publisher:
Release Date : 2014-05-14
Multidimensional Stochastic Processes As Rough Paths written by Peter K. Friz 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.
An introduction to rough path theory and its applications to stochastic analysis, written for graduate students and researchers.
A Course On Rough Paths
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Author : Peter K. Friz
language : en
Publisher: Springer Nature
Release Date : 2020-05-27
A Course On Rough Paths written by Peter K. Friz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-27 with Mathematics categories.
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Stochastic Analysis
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Author : Hiroyuki Matsumoto
language : en
Publisher: Cambridge University Press
Release Date : 2017
Stochastic Analysis written by Hiroyuki Matsumoto 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 with Mathematics categories.
Developing the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.
Stochastic Equations In Infinite Dimensions
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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2014-04-17
Stochastic Equations In Infinite Dimensions written by Giuseppe Da Prato 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 2014-04-17 with Mathematics categories.
Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
An Introduction To Computational Stochastic Pdes
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Author : Gabriel J. Lord
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-11
An Introduction To Computational Stochastic Pdes written by Gabriel J. Lord 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 2014-08-11 with Business & Economics categories.
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
Geometric Analysis
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Author : Peter Li
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-03
Geometric Analysis written by Peter Li 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 2012-05-03 with Mathematics categories.
This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.
Mathematical Aspects Of Quantum Field Theory
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Author : Edson de Faria
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Mathematical Aspects Of Quantum Field Theory written by Edson de Faria 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 2010-08-12 with Science categories.
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
The Theory Of Fusion Systems
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Author : David A. Craven
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-23
The Theory Of Fusion Systems written by David A. Craven 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 2011-06-23 with Mathematics categories.
The first book to deal comprehensively with the theory of fusion systems.
Enumerative Combinatorics Volume 1
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Author : Richard P. Stanley
language : en
Publisher: Cambridge University Press
Release Date : 2011-12-12
Enumerative Combinatorics Volume 1 written by Richard P. Stanley 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 2011-12-12 with Mathematics categories.
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.