{"product_id":"random-fields-and-stochastic-partial-differential-equations-von-y-rozanov","title":"Random Fields and Stochastic Partial Differential Equations","description":"This 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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792349846\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048150090\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792349846","offer_id":51344542342,"sku":"9780792349846","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048150090","offer_id":39415647666269,"sku":"9789048150090","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/ca325fd0-54c5-45a7-9ab0-d927fde9df76.jpg?v=1772175723","url":"https:\/\/shop.autorenwelt.de\/en\/products\/random-fields-and-stochastic-partial-differential-equations-von-y-rozanov","provider":"Autorenwelt Shop","version":"1.0","type":"link"}