{ "item_title" : "Random Fields and Stochastic Partial Differential Equations", "item_author" : [" Y. Rozanov "], "item_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.", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/9/04/815/009/9048150094_b.jpg", "price_data" : { "retail_price" : "109.99", "online_price" : "109.99", "our_price" : "109.99", "club_price" : "109.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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