دانلود کتاب A Course on Rough Paths: With an Introduction to Regularity Structures

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 inZentralblatt MATH

04021 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.1302Peter K. Friz is presently Einstein Professor of Mathematics at TU and WIAS Berlin. His previous professional affiliations include Cambridge University and Merrill Lynch, and he holds a PhD from the Courant Institute of New York University. He has made contributions to the understanding of the Navier-Stokes equation as dynamical system, pioneered new asymptotic techniques in financial mathematics and has written many influential papers on the applications of rough path theory to stochastic analysis, ranging from the interplay of rough paths with Malliavin calculus to a (rough-) pathwise view on non-linear SPDEs. Jointly with N. Victoir he authored a monograph on stochastic processes as rough paths.Martin Hairer KBE FRS is currently Professor of Mathematics at Imperial College London. He has mostly worked in the fields of stochastic partial differential equations in particular, and in stochastic analysis and stochastic dynamics in general. He made fundamental advances in various directions such as the study of hypoelliptic and/or hypocoercive diffusions, the development of an ergodic theory for stochastic PDEs, the systematisation of the construction of Lyapunov functions for stochastic systems, the development of a general theory of ergodicity for non-Markovian systems, multiscale analysis techniques, etc. Most recently, he has worked on applying rough path techniques to the analysis of certain ill-posed stochastic PDEs and introduced the theory of regularity structures. For this work he was awarded the Fields Medal at the 2014 ICM in Seoul.1802With 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 theMathematical 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 inZentralblatt MATH1902Provides a self-contained introduction to rough path analysis with many exercisesIncludes applications to stochastic partial differential equationsCovers the basics of the new theory of regularity structures060530001https://covers.springernature.com/boo...0101https://www.springer.com/978303041555601http://www.springer.com/01Springer Nature ImprintSPRSpringer0101SIPSpringer International Publishing01055251753Springer International PublishingChamCH0220200601202001WORLD080gr01235mm02155mm0303978331908331515978331908331501ISBN-13 hyphenated978-3-319-08331-5BC2703978303041556315978303041556301ISBN-13 hyphenated978-3-030-41556-3DGSpringer International Publishing01ROWNP102020060102Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00184.99AUDAU2020011601Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00177.26AUDAU2020011602Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00159.00CHFCHR2.52020011602Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00153.49EURDER72020011602Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00152.74EURFR2020011602Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00151.99EURIT2020011602Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00154.49EURNL2020011602Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00154.99EURATR102020011601Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00149.99EURROW2020011601Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB00144.99GBPGB2020011601Recommended Retail Price01BIC discount group codeASPVB002Product discount groupSPVB0013560.00INRIN20200116Springer International Publishing01US02YNP102020060101Recommended Retail Price01BIC discount group codeADGNY202Product discount groupDGNY20149.99EURROW2020011601Recommended Retail Price01BIC discount group codeADGNY202Product discount groupDGNY20159.99USDUS20200116