{"product_id":"rozanov-y-random-fields-and-stochastic-partial-differential-equations-9780792349846","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.","brand":"Springer","offers":[{"title":"Default Title","offer_id":54636744737110,"sku":null,"price":0.0,"currency_code":"EUR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0925\/5829\/5382\/files\/product_image_9780792349846_1.jpg?v=1791042048","url":"https:\/\/www.momoxbooks.com\/de\/products\/rozanov-y-random-fields-and-stochastic-partial-differential-equations-9780792349846","provider":"momox","version":"1.0","type":"link"}