03490nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118040002500153050001900178050001600197072001600213072002300229072001500252072001600267082001400283100008100297245011400378264007500492300004300567336002600610337002600636338003600662347002400698490002900722505023800751520144800989650003802437650003702475650012002512650010702632700008002739710003402819773002002853776003602873776003602909830002902945856004602974978-3-319-58647-2DE-He21320181204134424.0cr nn 008mamaa170706s2017 gw | s |||| 0|eng d a97833195864727 a10.1007/978-3-319-58647-22doi aISI Library, Kolkata 4aQA273.A1-274.9 4aQA274-274.9 7aPBT2bicssc 7aMAT0290002bisacsh 7aPBT2thema 7aPBWL2thema04a519.22231 aLototsky, Sergey V.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aStochastic Partial Differential Equationsh[electronic resource] /cby Sergey V. Lototsky, Boris L. Rozovsky. 1aCham :bSpringer International Publishing :bImprint: Springer,c2017. aXIV, 508 p. 1 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext,x0172-59390 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. 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. 0aDistribution (Probability theory. 0aDifferential equations, partial.14aProbability Theory and Stochastic Processes.0http://scigraph.springernature.com/things/product-market-codes/M2700424aPartial Differential Equations.0http://scigraph.springernature.com/things/product-market-codes/M121551 aRozovsky, Boris L.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978331958645808iPrinted edition:z9783319586465 0aUniversitext,x0172-593940uhttps://doi.org/10.1007/978-3-319-58647-2