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Random Fields and Stochastic Partial Differential Equations (Hardcover, 1998 ed.)
Loot Price: R3,227
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Random Fields and Stochastic Partial Differential Equations (Hardcover, 1998 ed.)
Series: Mathematics and Its Applications, 438
Expected to ship within 12 - 17 working days
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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
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