Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A Course on Rough Paths PDF full book. Access full book title A Course on Rough Paths by Peter K. Friz. Download full books in PDF and EPUB format.
Author: Peter K. Friz Publisher: Springer Nature ISBN: 3030415562 Category : Mathematics Languages : en Pages : 346
Book Description
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: Peter K. Friz Publisher: Springer Nature ISBN: 3030415562 Category : Mathematics Languages : en Pages : 346
Book Description
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: Peter K. Friz Publisher: Springer ISBN: 3319083325 Category : Mathematics Languages : en Pages : 262
Book Description
Lyons’ rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension – the theory of regularity structures – and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.
Author: Peter K. Friz Publisher: Springer ISBN: 9783030415556 Category : Mathematics Languages : en Pages : 346
Book Description
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: Springer ISBN: 3540712852 Category : Mathematics Languages : en Pages : 126
Book Description
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: Peter K. Friz Publisher: Cambridge University Press ISBN: 9780521876070 Category : Mathematics Languages : en Pages : 670
Book Description
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: Stephen Boyd Publisher: Cambridge University Press ISBN: 1316518965 Category : Business & Economics Languages : en Pages : 477
Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Daniel Abraham Publisher: Orbit ISBN: 0316175072 Category : Fiction Languages : en Pages : 460
Book Description
"Everything I look for in a fantasy." -- George R. R. Martin All paths lead to war. . . Marcus' hero days are behind him. He knows too well that even the smallest war still means somebody's death. When his men are impressed into a doomed army, staying out of a battle he wants no part of requires some unorthodox steps. Cithrin is an orphan, ward of a banking house. Her job is to smuggle a nation's wealth across a war zone, hiding the gold from both sides. She knows the secret life of commerce like a second language, but the strategies of trade will not defend her from swords. Geder, sole scion of a noble house, has more interest in philosophy than in swordplay. A poor excuse for a soldier, he is a pawn in these games. No one can predict what he will become. Falling pebbles can start a landslide. A spat between the Free Cities and the Severed Throne is spiraling out of control. A new player rises from the depths of history, fanning the flames that will sweep the entire region onto The Dragon's Path -- the path to war. The Dagger and the Coin The Dragon's Path The King's Blood The Tyrant's Law The Widow's House The Spider's War
Author: David Nualart Publisher: Cambridge University Press ISBN: 1107039126 Category : Business & Economics Languages : en Pages : 249
Book Description
A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Author: Huaizhong Zhao Publisher: World Scientific ISBN: 9814360910 Category : Mathematics Languages : en Pages : 458
Book Description
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
Author: Terry Lyons Publisher: Oxford University Press ISBN: 9780198506485 Category : Mathematics Languages : en Pages : 358
Book Description
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: Peter K. Friz
Author: Peter K. Friz
Author: Peter K. Friz
Author: Peter K. Friz
Author: Terry J. Lyons
Author: Peter K. Friz
Author: Stephen Boyd
Author: Daniel Abraham
Author: David Nualart
Author: Huaizhong Zhao
Author: Terry Lyons