Solving inverse problems for random equations and applications

Herb E. Kunze (), Davide La Torre and Edward R. Vrscay ()

Departmental Working Papers from Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano

Abstract: ABSTRACT: 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.

Keywords: Inverse problems; collage method; random differential equations (search for similar items in EconPapers)
Date: 2007-12-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:mil:wpdepa:2007-44

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