LEADER 00827nam0-22003131i-450- 001 990003281130403321 005 20001010 035 $a000328113 035 $aFED01000328113 035 $a(Aleph)000328113FED01 035 $a000328113 100 $a20000920d1956----km-y0itay50------ba 101 0 $aita 105 $ay-------001yy 200 1 $a<>BONIFICHE DI MACCARESE E DI ALBERESE 205 $a1 210 $aNapoli$cCNR$d1956 215 $app.150 610 0 $aMemorie di Geografia Economica 676 $a021.015 700 1$aDella Valle,$bCarlo$f<1902-1977>$065542 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990003281130403321 952 $a021.015.DEL$b9927$fDECGE 959 $aDECGE 996 $aBonifiche di Maccarese e di Alberese$9281494 997 $aUNINA DB $aING01 LEADER 01335nam 2200361 n 450 001 996393382703316 005 20200824121717.0 035 $a(CKB)4940000000114021 035 $a(EEBO)2240903431 035 $a(UnM)ocm99888856e 035 $a(UnM)99888856 035 $a(EXLCZ)994940000000114021 100 $a19990302d1681 uy 101 0 $aeng 135 $aurbn||||a|bb| 200 13$aAn account of the tryal of Mr. Stephen Colledge at Oxford, August the 17th 1681. 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Chekroun, Honghu Liu, Shouhong Wang 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (141 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 08$a3-319-12519-2 320 $aIncludes bibliographical references and index. 327 $aGeneral Introduction -- Preliminaries -- Invariant Manifolds -- Pullback Characterization of Approximating, and Parameterizing Manifolds -- Non-Markovian Stochastic Reduced Equations -- On-Markovian Stochastic Reduced Equations on the Fly -- Proof of Lemma 5.1.-References -- Index. 330 $aIn this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aDifferential equations, Partial 606 $aDynamics 606 $aErgodic theory 606 $aProbabilities 606 $aDifferential equations 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aDifferential equations, Partial. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aProbabilities. 615 0$aDifferential equations. 615 14$aPartial Differential Equations. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aProbability Theory and Stochastic Processes. 615 24$aOrdinary Differential Equations. 676 $a519.22 700 $aChekroun$b Mickae?l D.$4aut$4http://id.loc.gov/vocabulary/relators/aut$00 702 $aLiu$b Honghu$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWang$b Shouhong$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299781803321 996 $aStochastic Parameterizing Manifolds and Non-Markovian Reduced Equations$92512144 997 $aUNINA