{"product_id":"9783319125190","title":"SpringerBriefs in Mathematics: Stochastic Manifolds for Nonlinear SPDEs II","description":"\u003ch1\u003eSpringerBriefs in Mathematics: Stochastic Manifolds for Nonlinear SPDEs II\u003c\/h1\u003e \u003ch2\u003eChekroun, Mickaël D.; Liu, Honghu; Wang, Shouhong\u003c\/h2\u003e \u003cp\u003eIn 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2015-01-14\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319125190\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-12520-6\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 129\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45548564152460,"sku":"9783319125190","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319125190.jpg?v=1775785796","url":"https:\/\/lateknightbooks.com\/products\/9783319125190","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}