Stochastic Cauchy Problems in Infinite Dimensions: Generalized and
Regularized Solutions presents stochastic differential equations
for random processes with values in Hilbert spaces. Accessible to
non-specialists, the book explores how modern semi-group and
distribution methods relate to the methods of infinite-dimensional
stochastic analysis. It also shows how the idea of regularization
in a broad sense pervades all these methods and is useful for
numerical realization and applications of the theory. The book
presents generalized solutions to the Cauchy problem in its initial
form with white noise processes in spaces of distributions. It also
covers the "classical" approach to stochastic problems involving
the solution of corresponding integral equations. The first part of
the text gives a self-contained introduction to modern semi-group
and abstract distribution methods for solving the homogeneous
(deterministic) Cauchy problem. In the second part, the author
solves stochastic problems using semi-group and distribution
methods as well as the methods of infinite-dimensional stochastic
analysis.
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