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 forthe 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 ReviewsIt 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
