Solving inverse problems for random equations and applications
AbstractABSTRACT: Most natural phenomena are subject to small variations in the environment within which they take place; 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 T(w,x(w))=x(w) as random fixed point equations, where T:Y x X -> X is a given operator, Y is a probability space and (X,d) 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.
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Bibliographic InfoPaper provided by Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano in its series Departmental Working Papers with number 2007-44.
Date of creation: 01 Dec 2007
Date of revision:
Inverse problems; collage method; random differential equations;
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