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Inverse problems for random differential equations using the collage method for random contraction mappings

Author

Listed:
  • Davide La Torre

    (University of Milan)

  • Herb Kunze
  • Ed Vrscay

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 & Ed Vrscay, 2006. "Inverse problems for random differential equations using the collage method for random contraction mappings," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1036, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1036
    Note: oai:cdlib1:unimi-1036
    as

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    Cited by:

    1. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers 2009_30, Business School - Economics, University of Glasgow.
    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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