TY  - BOOK
AU  - Friz, Peter K.
AU  - Hairer, Martin
TI  - Course on rough paths : : with an introduction to regularity structures
T2  - Universitext, 
SN  - 9783030415556
U1  - 519.21 
PY  - 2020///
CY  - Cham, Switzerland
PB  - Springer
KW  - Stochastic differential equations
KW  - Stochastic analysis
KW  - Rough paths
KW  - Robust stochastic integration
KW  - Gaussian processes
KW  - Partial differential equations
N1  - Includes bibliographical references and index
N2  - 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
UR  - https://link.springer.com/content/pdf/bfm:978-3-030-41556-3/1
UR  - https://www.goodreads.com/book/show/50690515-a-course-on-rough-paths?ref=nav_sb_ss_1_13#CommunityReviews
ER  -