Inverse problems for random differential equations using the collage method for random contraction mappings
Davide La Torre, University of Milan
Herb Kunze
Ed Vrscay
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ABSTRACT:
Most natural phenomena or the experiments that explore
them are subject to small variations in the environment within which
they take place. As a result, data gathered from many runs of the same
experiment may well show differences that are most suitably accounted
for by a model that incorporates some randomness. Differential equations
with random coefficients are one such class of useful models. In this paper
we consider such equations as random fixed point equations T(w,x(w)) =
x(w), where T : \Omega × X \to X is a random integral operator, \Omega is a
probability space and X is a complete metric space. We consider the
following inverse problem for such equations: given a set of realizations of
the fixed point of T (possibly the interpolations of different observational
data sets), determine the operator T or the mean value of its random
components, as appropriate. We solve the inverse problem for this class
of equations by using the collage theorem.
SUGGESTED CITATION:
Davide La Torre, Herb Kunze, and Ed Vrscay,
"Inverse problems for random differential equations using the collage method for random contraction mappings"
(September 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 16.
http://services.bepress.com/unimi/statistics/art16
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