{"product_id":"9780792349846","title":"Mathematics and Its Applications","description":"\u003ch1\u003eMathematics and Its Applications\u003c\/h1\u003e \u003ch2\u003eRozanov, Y.\u003c\/h2\u003e \u003cp\u003eThis book considers some models described by means of partial dif­ ferential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equa­ tions an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. {The term \"stochastic\" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source\"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri­ ate random field\"' with independent values, i. e. , generalized random function\"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain \"roughness\" of the ran­ dom field \"' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of non­ linear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1998-03-31\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792349846\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-017-2838-6\u003c\/p\u003e \u003cp\u003eDimensions: 234cm x156cm\u003c\/p\u003e \u003cp\u003ePages: 232\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46539692867724,"sku":"9780792349846","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792349846.jpg?v=1775679031","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780792349846","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}