LEADER 04369nam 22006855 450 001 9910299967303321 005 20250609110740.0 010 $a3-319-08332-5 024 7 $a10.1007/978-3-319-08332-2 035 $a(CKB)3710000000227351 035 $a(SSID)ssj0001338678 035 $a(PQKBManifestationID)11704396 035 $a(PQKBTitleCode)TC0001338678 035 $a(PQKBWorkID)11338077 035 $a(PQKB)11358154 035 $a(DE-He213)978-3-319-08332-2 035 $a(MiAaPQ)EBC5587772 035 $a(Au-PeEL)EBL5587772 035 $a(OCoLC)890462092 035 $a(PPN)180627139 035 $a(MiAaPQ)EBC1802580 035 $a(EXLCZ)993710000000227351 100 $a20140826d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 12$aA Course on Rough Paths $eWith an Introduction to Regularity Structures /$fby Peter K. Friz, Martin Hairer 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XIV, 251 p. 2 illus.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-08331-7 327 $aIntroduction -- The space of rough paths -- Brownian motion as a rough path -- Integration against rough paths -- Stochastic integration and It?o?s formula -- Doob?Meyer type decomposition for rough paths -- Operations on controlled rough paths -- Solutions to rough differential equations -- Stochastic differential equations -- Gaussian rough paths -- Cameron?Martin regularity and applications -- Stochastic partial differential equations -- Introduction to regularity structures -- Operations on modelled distributions -- Application to the KPZ equation. 330 $aLyons? rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension ? the theory of regularity structures ? and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aDifferential equations 606 $aDifferential equations, Partial 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$aDifferential equations. 615 0$aDifferential equations, Partial. 615 14$aProbability Theory and Stochastic Processes. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 676 $a519.2 700 $aFriz$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 $a9910299967303321 996 $aA Course on Rough Paths$92052317 997 $aUNINA