{"product_id":"stochastic-parameterizing-manifolds-and-non-markovian-reduced-equations-von-mickael-d-chekroun-shouhong-wang-und-honghu-liu","title":"Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations","description":"In 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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783319125190\"\u003e\u003ch3\u003eStochastic Manifolds for Nonlinear SPDEs II\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783319125190","offer_id":40080052551773,"sku":"9783319125190","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/67bc16d5-2a20-428d-8086-b2c8af55c76f.jpg?v=1772170516","url":"https:\/\/shop.autorenwelt.de\/products\/stochastic-parameterizing-manifolds-and-non-markovian-reduced-equations-von-mickael-d-chekroun-shouhong-wang-und-honghu-liu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}