English, Article, Journal or magazine article edition: Solving inverse problems for random equations and applications Herb E. KUNZE; Davide LA TORRE; Edward R. VRSCAY

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Bookmark: http://trove.nla.gov.au/version/58666
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Solving inverse problems for random equations and applications
Author
  • Herb E. KUNZE
  • Davide LA TORRE
  • Edward R. VRSCAY
Physical Description
  • preprint
Notes
  • 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.
  • Inverse problems, collage method, random differential equations
  • RePEc:mil:wpdepa:2007-44
Language
  • English
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