Home
Random Fields and Stochastic Partial Differential Equations / Edition 1
Barnes and Noble
Random Fields and Stochastic Partial Differential Equations / Edition 1
Current price: $109.99
Barnes and Noble
Random Fields and Stochastic Partial Differential Equations / Edition 1
Current price: $109.99
Size: OS
Loading Inventory...
*Product information may vary - to confirm product availability, pricing, shipping and return information please contact Barnes and Noble
This book considers some models described by means of partial dif ferential equations and boundary conditions with chaotic shastic disturbance. In a framework of shastic Partial Differential Equa tions an approach is suggested to generalize solutions of shastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding shastic Sobolev spaces. {The term "shastic" 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 (shastic) 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.