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Solving inverse problems for random equations and applications

Author

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  • Herb E. KUNZE
  • Davide LA TORRE
  • Edward R. VRSCAY

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.

Suggested Citation

  • Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2007. "Solving inverse problems for random equations and applications," Departmental Working Papers 2007-44, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2007-44
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    File URL: http://wp.demm.unimi.it/files/wp/2007/DEMM-2007_044wp.pdf
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    Cited by:

    1. La Torre, Davide & Marsiglio, Simone, 2010. "Endogenous technological progress in a multi-sector growth model," Economic Modelling, Elsevier, vol. 27(5), pages 1017-1028, September.
    2. Alberto BUCCI & Herb E. KUNZE & Davide LA TORRE, 2008. "Parameter identification, population and economic growth in an extended Lucas and Uzawa-type two sector model," Departmental Working Papers 2008-34, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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    Keywords

    Inverse problems; collage method; random differential equations;
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