A Course On Rough Paths

Author : Peter K. Friz,Martin Hairer
Publisher : Springer Nature
Page : 346 pages
File Size : 42,6 Mb
Release : 2020-05-27
Category : Mathematics
ISBN : 9783030415563

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A Course on Rough Paths by Peter K. Friz,Martin Hairer Pdf

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,Michael J. Caruana,Thierry Lévy
Publisher : Springer
Page : 126 pages
File Size : 51,5 Mb
Release : 2007-04-25
Category : Mathematics
ISBN : 9783540712855

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Differential Equations Driven by Rough Paths by Terry J. Lyons,Michael J. Caruana,Thierry Lévy Pdf

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,Nicolas B. Victoir
Publisher : Cambridge University Press
Page : 670 pages
File Size : 48,9 Mb
Release : 2010-02-04
Category : Mathematics
ISBN : 0521876079

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Multidimensional Stochastic Processes as Rough Paths by Peter K. Friz,Nicolas B. Victoir Pdf

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 : David Nualart,Eulalia Nualart
Publisher : Cambridge University Press
Page : 249 pages
File Size : 55,6 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781107039124

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Introduction to Malliavin Calculus by David Nualart,Eulalia Nualart Pdf

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Author : Tom Coyne
Publisher : Simon and Schuster
Page : 416 pages
File Size : 54,7 Mb
Release : 2022-05-17
Category : Biography & Autobiography
ISBN : 9781982128067

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A Course Called America by Tom Coyne Pdf

In 'A Course Called America', Tom Coyne plays his way across the United States in search of the great American golf course. Packed with fascinating tales from American golf history, comic road misadventures, illuminating insight into course design, and many a memorable round with local golfers, this book is an epic narrative travelogue brimming with heart and soul.

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 53,8 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 117 pages
File Size : 55,9 Mb
Release : 1991-08-07
Category : Computers
ISBN : 9780262326452

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Basic Category Theory for Computer Scientists by Benjamin C. Pierce Pdf

Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading

Author : Anonim
Publisher : Univalent Foundations
Page : 484 pages
File Size : 51,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 8210379456XXX

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Homotopy Type Theory: Univalent Foundations of Mathematics by Anonim Pdf

Author : Terry Lyons,Wallis Professor of Mathematics Terry Lyons,Zhongmin Qian
Publisher : Oxford University Press
Page : 358 pages
File Size : 53,8 Mb
Release : 2002
Category : Mathematics
ISBN : 0198506481

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System Control and Rough Paths by Terry Lyons,Wallis Professor of Mathematics Terry Lyons,Zhongmin Qian Pdf

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 Friz,Wolfgang König,Chiranjib Mukherjee,Stefano Olla
Publisher : Springer
Page : 294 pages
File Size : 44,5 Mb
Release : 2019-05-24
Category : Mathematics
ISBN : 9783030153380

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Probability and Analysis in Interacting Physical Systems by Peter Friz,Wolfgang König,Chiranjib Mukherjee,Stefano Olla Pdf

This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15–19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics.

Author : Brad Taylor
Publisher : Dutton
Page : 578 pages
File Size : 44,6 Mb
Release : 2012-01-03
Category : Fiction
ISBN : 9780451413192

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One Rough Man by Brad Taylor Pdf

Vince Flynn and Brad Thor, move over: introducing a pulse-pounding new international thriller series by a former Delta Force commander.

Author : Daniel Abraham
Publisher : Orbit
Page : 460 pages
File Size : 54,8 Mb
Release : 2011-04-07
Category : Fiction
ISBN : 9780316175074

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The Dragon's Path by Daniel Abraham Pdf

"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 : Michael J. Caruana
Publisher : Springer Verlag
Page : 109 pages
File Size : 46,7 Mb
Release : 2007-06-12
Category : Mathematics
ISBN : 3540712844

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Differential Equations Driven by Rough Paths by Michael J. Caruana Pdf

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 : Fabrice Baudoin
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 292 pages
File Size : 46,8 Mb
Release : 2014
Category : Calculus
ISBN : 3037191333

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Diffusion Processes and Stochastic Calculus by Fabrice Baudoin Pdf

The main purpose of the book is to present, at a graduate level and in a self-contained way, the most important aspects of the theory of continuous stochastic processes in continuous time and to introduce some of its ramifications such as the theory of semigroups, the Malliavin calculus, and the Lyons' rough paths. This book is intended for students, or even researchers, who wish to learn the basics in a concise but complete and rigorous manner. Several exercises are distributed throughout the text to test the understanding of the reader and each chapter ends with bibliographic comments aimed at those interested in exploring the materials further. Stochastic calculus was developed in the 1950s and the range of its applications is huge and still growing today. Besides being a fundamental component of modern probability theory, domains of applications include but are not limited to: mathematical finance, biology, physics, and engineering sciences. The first part of the text is devoted to the general theory of stochastic processes. The author focuses on the existence and regularity results for processes and on the theory of martingales. This allows him to introduce the Brownian motion quickly and study its most fundamental properties. The second part deals with the study of Markov processes, in particular, diffusions. The author's goal is to stress the connections between these processes and the theory of evolution semigroups. The third part deals with stochastic integrals, stochastic differential equations and Malliavin calculus. In the fourth and final part, the author presents an introduction to the very new theory of rough paths by Terry Lyons.

Author : Christian Bayer,Peter K. Friz,Masaaki Fukasawa,Jim Gatheral,Antoine Jacquier,Mathieu Rosenbaum
Publisher : SIAM
Page : 292 pages
File Size : 44,7 Mb
Release : 2023-12-18
Category : Mathematics
ISBN : 9781611977783

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Rough Volatility by Christian Bayer,Peter K. Friz,Masaaki Fukasawa,Jim Gatheral,Antoine Jacquier,Mathieu Rosenbaum Pdf

Volatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. The mathematical description of the volatility process has been an active topic of research for decades; however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility behaves essentially as a fractional Brownian motion with a small Hurst parameter. The first book to offer a comprehensive exploration of the subject, Rough Volatility contributes to the understanding and application of rough volatility models by equipping readers with the tools and insights needed to delve into the topic, exploring the motivation for rough volatility modeling, providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject’s development and progression. This book is designed for researchers and graduate students in quantitative finance as well as quantitative analysts and finance professionals.