Path Integrals For Stochastic Processes An Introduction

Download Path Integrals For Stochastic Processes An Introduction full books in PDF, epub, and Kindle. Read online Path Integrals For Stochastic Processes An Introduction ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Path Integrals for Stochastic Processes

Author : Horacio S. Wio
Publisher : World Scientific
ISBN 13 : 9814449040
Total Pages : 174 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Path Integrals for Stochastic Processes by : Horacio S. Wio

Download or read book Path Integrals for Stochastic Processes written by Horacio S. Wio and published by World Scientific. This book was released on 2013 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.

Path Integrals For Stochastic Processes: An Introduction

Author : Horacio Sergio Wio
Publisher : World Scientific
ISBN 13 : 9814449059
Total Pages : 174 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Path Integrals For Stochastic Processes: An Introduction by : Horacio Sergio Wio

Download or read book Path Integrals For Stochastic Processes: An Introduction written by Horacio Sergio Wio and published by World Scientific. This book was released on 2013-01-18 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations. remove /a

Path Integrals in Physics

Author : M Chaichian
Publisher : CRC Press
ISBN 13 : 9780367397142
Total Pages : 336 pages
Book Rating : 4.3/5 (971 download)

DOWNLOAD NOW!

Book Synopsis Path Integrals in Physics by : M Chaichian

Download or read book Path Integrals in Physics written by M Chaichian and published by CRC Press. This book was released on 2019-08-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.

Path Integrals and Quantum Processes

Author : Mark S. Swanson
Publisher : Courier Corporation
ISBN 13 : 0486782301
Total Pages : 463 pages
Book Rating : 4.4/5 (867 download)

DOWNLOAD NOW!

Book Synopsis Path Integrals and Quantum Processes by : Mark S. Swanson

Download or read book Path Integrals and Quantum Processes written by Mark S. Swanson and published by Courier Corporation. This book was released on 2014-02-19 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.

Introduction to Stochastic Integration

Author : Hui-Hsiung Kuo
Publisher : Springer Science & Business Media
ISBN 13 : 0387310576
Total Pages : 290 pages
Book Rating : 4.3/5 (873 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Stochastic Integration by : Hui-Hsiung Kuo

Download or read book Introduction to Stochastic Integration written by Hui-Hsiung Kuo and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews: "Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY

Mathematical Theory of Feynman Path Integrals

Author : Sergio A. Albeverio
Publisher : Springer
ISBN 13 : 354038250X
Total Pages : 143 pages
Book Rating : 4.5/5 (43 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Theory of Feynman Path Integrals by : Sergio A. Albeverio

Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio A. Albeverio and published by Springer. This book was released on 2006-11-14 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Feynman path integrals integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low dimensional topology and differential geometry, algebraic geometry, infinite dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments which have occurred since then, an entire new chapter about the current forefront of research has been added. Except for this new chapter, the basic material and presentation of the first edition was mantained, a few misprints have been corrected. At the end of each chapter the reader will also find notes with further bibliographical information.

Stochastic Processes in Cell Biology

Author : Paul C. Bressloff
Publisher : Springer Nature
ISBN 13 : 3030725154
Total Pages : 773 pages
Book Rating : 4.0/5 (37 download)

DOWNLOAD NOW!

Book Synopsis Stochastic Processes in Cell Biology by : Paul C. Bressloff

Download or read book Stochastic Processes in Cell Biology written by Paul C. Bressloff and published by Springer Nature. This book was released on 2022-01-04 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes – Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

Brownian Motion

Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110307308
Total Pages : 424 pages
Book Rating : 4.1/5 (13 download)

DOWNLOAD NOW!

Book Synopsis Brownian Motion by : René L. Schilling

Download or read book Brownian Motion written by René L. Schilling and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-06-18 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

Feynman's Thesis

Author : Richard Phillips Feynman
Publisher : World Scientific
ISBN 13 : 9812563660
Total Pages : 142 pages
Book Rating : 4.8/5 (125 download)

DOWNLOAD NOW!

Book Synopsis Feynman's Thesis by : Richard Phillips Feynman

Download or read book Feynman's Thesis written by Richard Phillips Feynman and published by World Scientific. This book was released on 2005 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.

Mathematical Feynman Path Integrals And Their Applications

Author : Sonia Mazzucchi
Publisher : World Scientific
ISBN 13 : 9814469270
Total Pages : 225 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Feynman Path Integrals And Their Applications by : Sonia Mazzucchi

Download or read book Mathematical Feynman Path Integrals And Their Applications written by Sonia Mazzucchi and published by World Scientific. This book was released on 2009-05-22 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman's ideas.This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author.Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.

Stochastic Processes and Applications

Author : Grigorios A. Pavliotis
Publisher : Springer
ISBN 13 : 1493913239
Total Pages : 345 pages
Book Rating : 4.4/5 (939 download)

DOWNLOAD NOW!

Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

An Introduction to Stochastic Differential Equations

Author : Lawrence C. Evans
Publisher : American Mathematical Soc.
ISBN 13 : 1470410540
Total Pages : 161 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis An Introduction to Stochastic Differential Equations by : Lawrence C. Evans

Download or read book An Introduction to Stochastic Differential Equations written by Lawrence C. Evans and published by American Mathematical Soc.. This book was released on 2012-12-11 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

Author : Hagen Kleinert
Publisher : World Scientific
ISBN 13 : 9814273570
Total Pages : 1626 pages
Book Rating : 4.8/5 (142 download)

DOWNLOAD NOW!

Book Synopsis Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by : Hagen Kleinert

Download or read book Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets written by Hagen Kleinert and published by World Scientific. This book was released on 2009 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

Basic Stochastic Processes

Author : Zdzislaw Brzezniak
Publisher : Springer Science & Business Media
ISBN 13 : 9783540761754
Total Pages : 244 pages
Book Rating : 4.7/5 (617 download)

DOWNLOAD NOW!

Book Synopsis Basic Stochastic Processes by : Zdzislaw Brzezniak

Download or read book Basic Stochastic Processes written by Zdzislaw Brzezniak and published by Springer Science & Business Media. This book was released on 2000-07-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

Essentials of Stochastic Processes

Author : Richard Durrett
Publisher : Springer
ISBN 13 : 3319456148
Total Pages : 282 pages
Book Rating : 4.3/5 (194 download)

DOWNLOAD NOW!

Book Synopsis Essentials of Stochastic Processes by : Richard Durrett

Download or read book Essentials of Stochastic Processes written by Richard Durrett and published by Springer. This book was released on 2016-11-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.

Introduction to Stochastic Calculus with Applications

Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

A Course on Rough Paths

Author : Peter K. Friz
Publisher : Springer Nature
ISBN 13 : 3030415562
Total Pages : 354 pages
Book Rating : 4.0/5 (34 download)

DOWNLOAD NOW!

Book Synopsis A Course on Rough Paths by : Peter K. Friz

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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