LEADER 03705nam 22005655 450 001 9910254276203321 005 20200703040543.0 010 $a3-319-58647-5 024 7 $a10.1007/978-3-319-58647-2 035 $a(DE-He213)978-3-319-58647-2 035 $a(MiAaPQ)EBC6310734 035 $a(MiAaPQ)EBC5592275 035 $a(Au-PeEL)EBL5592275 035 $a(OCoLC)993876752 035 $a(PPN)203669150 035 $a(CKB)4340000000062052 035 $a(EXLCZ)994340000000062052 100 $a20170706d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Partial Differential Equations /$fby Sergey V. Lototsky, Boris L. Rozovsky 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIV, 508 p. 1 illus.) 225 1 $aUniversitext,$x0172-5939 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Basic Ideas -- Stochastic Analysis in Infinite Dimensions -- Linear Equations: Square-Integrable Solutions -- The Polynomial Chaos Method -- Parameter Estimation for Diagonal SPDEs -- Solutions -- References -- Index. 330 $aTaking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aPartial differential equations 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aProbabilities. 615 0$aPartial differential equations. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 676 $a519.22 700 $aLototsky$b Sergey V$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767168 702 $aRozovsky$b Boris L$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254276203321 996 $aStochastic Partial Differential Equations$92174091 997 $aUNINA