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A Course on Rough Paths - With an Introduction to Regularity Structures (Paperback, 2nd ed. 2020)
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A Course on Rough Paths - With an Introduction to Regularity Structures (Paperback, 2nd ed. 2020)
Series: Universitext
Expected to ship within 10 - 15 working days
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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 Ito-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
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