Random Fields and Stochastic Partial Differential Equations (eBook)

Y. Rozanov (Autor)

eBook Download: PDF

2013
Springer Netherlands (Verlag)
978-94-017-2838-6 (ISBN)

Infos

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 "e;stochastic"e; 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"e;' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri- ate random field"e;' with independent values, i. e. , generalized random function"e;' = ( 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 "e;roughness"e; of the ran- dom field "e;' 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.

Produkt-Details

• Erscheint lt. Verlag: 17.4.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• ISBN-10: 94-017-2838-0 / 9401728380
• ISBN-13: 978-94-017-2838-6 / 9789401728386