LEADER 04567nam 22006015 450 001 9910484562503321 005 20200630120230.0 010 $a3-030-41556-2 024 7 $a10.1007/978-3-030-41556-3 035 $a(CKB)4100000011273706 035 $a(MiAaPQ)EBC6212328 035 $a(DE-He213)978-3-030-41556-3 035 $a(PPN)248395033 035 $a(EXLCZ)994100000011273706 100 $a20200527d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Course on Rough Paths $eWith an Introduction to Regularity Structures /$fby Peter K. Friz, Martin Hairer 205 $a2nd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (354 pages) $cillustrations 225 1 $aUniversitext,$x0172-5939 311 $a3-030-41555-4 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aWith many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ? A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aDifferential equations 606 $aPartial differential equations 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aProbabilities. 615 0$aDifferential equations. 615 0$aPartial differential equations. 615 14$aProbability Theory and Stochastic Processes. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 676 $a519.2 676 $a519.22 700 $aFriz$b Peter K$4aut$4http://id.loc.gov/vocabulary/relators/aut$0480232 702 $aHairer$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484562503321 996 $aA Course on Rough Paths$92052317 997 $aUNINA