Random Fields and Stochastic Partial Differential Equations (Paperback)

Y. Rozanov

ISBN 10: 9048150094 / ISBN 13: 9789048150090

Published by Springer, Dordrecht, 2010

About this Item

Paperback. This book considers some models described by means of partial differential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic partial differential equations an approach is suggested to generalise solutions of stochastic boundary problems. The main topic concerns probabilistic aspects with applications to the most well-known random fields models which are representative for the corresponding stochastic Sobolev spaces. This work assumes basic knowledge of general analysis and probability, such as Hilbert space methods, Schwartz distributions, and Fourier transforms. Audience: This volume will be of interest to researchers and postgraduate students whose work involves probability theory, stochastic processes and partial differential equations. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

• Title: Random Fields and Stochastic Partial Differential Equations (Paperback)
• Publisher: Springer, Dordrecht
• Publication Date: 2010
• Language: English
• ISBN 10: 9048150094
• ISBN 13: 9789048150090
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

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.