TY - BOOK AU - Friz,Peter K. AU - Hairer, Martin. TI - Course on rough paths: with an introduction to regularity structures T2 - Universitext SN - 9783319083315 U1 - 519.2 23 PY - 2014/// CY - Switzerland PB - Springer KW - Stochastic differential equations. KW - Mathematics. KW - Probability Theory and Stochastic Processes N1 - Includes bibliographical references and index; 1. Introduction -- 2. The space of rough paths -- 3. Brownian motion as a rough path -- 4. Integration against rough paths -- 5. Stochastic integration and Itô's formula -- 6. Doob-Meyer type decomposition for rough paths -- 7. Operations on controlled rough paths -- 8. Solutions to rough differential equations -- 9. Stochastic differential equations -- 10. Gaussian rough paths -- 11. Cameron-Martin regularity and applications -- 12. Stochastic partial differential equations -- 13. Introduction to regularity structures -- 14. Operations on modelled distributions -- 15. Application to the KPZ equation-- References-- Index N2 - This book presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension - the theory of regularity structures - and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background. ER -