Random fixed point equations and inverse problems by collage theorem
Davide La Torre, University of Milan
Herb Kunze
Edward Vrscay
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ABSTRACT:
In this paper we are interested in the direct and inverse problems for the
following class of random fixed point equations $T(w,x(w))=x(w)$ where
$T:\Omega\times X\to X$ is a given operator, $\Omega$ is a probability space
and $X$ is a complete metric space. The inverse problem is solved by recourse
to the collage theorem for contractive maps. We then consider two applications:
(i) random integral equations and (ii) random iterated function systems with
greyscale maps (RIFSM), for which noise is added to the classical IFSM.
SUGGESTED CITATION:
Davide La Torre, Herb Kunze, and Edward Vrscay,
"Random fixed point equations and inverse problems by collage theorem"
(June 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 11.
http://services.bepress.com/unimi/statistics/art11
Paper presented by Pieralda Ferrari.
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