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Random Fields and Stochastic Partial Differential Equations (Paperback, Softcover reprint of hardcover 1st ed. 1998) Loot Price: R2,873
Discovery Miles 28 730
Random Fields and Stochastic Partial Differential Equations (Paperback, Softcover reprint of hardcover 1st ed. 1998): Y. Rozanov

Random Fields and Stochastic Partial Differential Equations (Paperback, Softcover reprint of hardcover 1st ed. 1998)

Y. Rozanov

Series: Mathematics and Its Applications, 438

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Loot Price R2,873 Discovery Miles 28 730 | Repayment Terms: R269 pm x 12*

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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.

General

Imprint: Springer
Country of origin: Netherlands
Series: Mathematics and Its Applications, 438
Release date: December 2010
First published: 1998
Authors: Y. Rozanov
Dimensions: 240 x 160 x 13mm (L x W x T)
Format: Paperback
Pages: 232
Edition: Softcover reprint of hardcover 1st ed. 1998
ISBN-13: 978-90-481-5009-0
Categories: Books > Science & Mathematics > Mathematics > Probability & statistics
Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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LSN: 90-481-5009-4
Barcode: 9789048150090

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