Differential Equations Driven By Rough Paths PDF Download
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Author | : Terry J. Lyons |
Publisher | : Springer |
Total Pages | : 126 |
Release | : 2007-04-25 |
Genre | : Mathematics |
ISBN | : 3540712852 |
Download Differential Equations Driven by Rough Paths Book in PDF, ePub and Kindle
Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory. The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths.
Author | : Michael J. Caruana |
Publisher | : Springer Verlag |
Total Pages | : 109 |
Release | : 2007-06-12 |
Genre | : Mathematics |
ISBN | : 9783540712848 |
Download Differential Equations Driven by Rough Paths Book in PDF, ePub and Kindle
Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory. The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths. The proofs are similar to those in the existing literature, but have been refined with the benefit of hindsight. The theory of rough paths aims to create the appropriate mathematical framework for expressing the relationships between evolving systems, by extending classical calculus to the natural models for noisy evolving systems, which are often far from differentiable.
Author | : Peter K. Friz |
Publisher | : Springer Nature |
Total Pages | : 346 |
Release | : 2020-05-27 |
Genre | : Mathematics |
ISBN | : 3030415562 |
Download A Course on Rough Paths Book in PDF, ePub and Kindle
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
Author | : Terry J. Lyons |
Publisher | : |
Total Pages | : 140 |
Release | : 2007 |
Genre | : Differential equations |
ISBN | : |
Download Differential Equations Driven by Rough Paths Book in PDF, ePub and Kindle
Author | : Peter K. Friz |
Publisher | : Cambridge University Press |
Total Pages | : 670 |
Release | : 2010-02-04 |
Genre | : Mathematics |
ISBN | : 9780521876070 |
Download Multidimensional Stochastic Processes as Rough Paths Book in PDF, ePub and Kindle
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.
Author | : Terry Lyons |
Publisher | : Oxford University Press |
Total Pages | : 358 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780198506485 |
Download System Control and Rough Paths Book in PDF, ePub and Kindle
This work describes a completely novel mathematical development which has already influenced probability theory, and has potential for application to engineering and to areas of pure mathematics: the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli.
Author | : Wilfried Grecksch |
Publisher | : World Scientific |
Total Pages | : 261 |
Release | : 2020-04-22 |
Genre | : Science |
ISBN | : 9811209804 |
Download Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics Book in PDF, ePub and Kindle
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Author | : Hiroshi Kunita |
Publisher | : Cambridge University Press |
Total Pages | : 364 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9780521599252 |
Download Stochastic Flows and Stochastic Differential Equations Book in PDF, ePub and Kindle
The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows.The classical theory was initiated by K. Itô and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby Itô's theory as a special case. The book can be used with advanced courses on probability theory or for self-study.
Author | : Kai Diethelm |
Publisher | : Springer |
Total Pages | : 251 |
Release | : 2010-08-18 |
Genre | : Mathematics |
ISBN | : 3642145744 |
Download The Analysis of Fractional Differential Equations Book in PDF, ePub and Kindle
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Author | : Xiaoying Han |
Publisher | : Springer |
Total Pages | : 250 |
Release | : 2017-10-25 |
Genre | : Mathematics |
ISBN | : 981106265X |
Download Random Ordinary Differential Equations and Their Numerical Solution Book in PDF, ePub and Kindle
This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.