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(ω,x(ω))=x(ω). Here T:Ω×X→X is a random integral operator, Ω 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

Inverse problems for random differential equations using the collage method for random contraction mappings / H. Kunze, D. La Torre, E.R. Vrscay. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - 223:2(2009 Jan 15), pp. 853-861.

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

#### 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(ω,x(ω))=x(ω). Here T:Ω×X→X is a random integral operator, Ω 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
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Collage theorem; Inverse problems; Random differential equations; Random fixed point equations; Random integral equations
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/52684`
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