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Random Fields and Stochastic Partial Differential Equations by Y. Rozanov

Random Fields and Stochastic Partial Differential Equations

by Y. Rozanov
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Book cover type: Hardcover
  • ISBN13: 9780792349846
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 232
  • Original Price: EUR 99.99
  • Language: English
  • Edition: 1998
  • Item Weight: 518 grams
  • BISAC Subject(s): Differential Equations / General and Probability & Statistics / General

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.

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