Random Fields and Stochastic Partial Differential Equations (Mathematics and Its Applications, 438)

Rozanov, Y.

ISBN 10: 0792349849 / ISBN 13: 9780792349846

Published by Springer, 1998

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Bibliographic Details

• Title: Random Fields and Stochastic Partial Differential Equations (Mathematics and Its Applications, 438)
• Publisher: Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 0792349849
• ISBN 13: 9780792349846
• Binding: Hardcover
• Condition: New

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Synopsis

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.

Language Notes

Text: English (translation)
Original Language: Russian