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

  • Authors:

  • H. E. Kunze;D. La Torre;E. R. Vrscay

  • Affiliations:

  • Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada;Department of Economics, Business and Statistics, University of Milan, Italy;Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

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Abstract

In this paper we are concerned with differential equations with random coefficients which will be considered as random fixed point equations of the form T(@w,x(@w))=x(@w), @w@?@W. Here T:@WxX-X is a random integral operator, (@W,F,P) 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 for contraction mappings.