# Random fixed point equations and inverse problems by collage theorem

*Davide La Torre* (),
*Herb Kunze* and
*Edward Vrscay*

No unimi-1030, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

**Abstract:**
In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations $T(w,x(w))=x(w)$ where $T:\Omega\times X\to X$ is a given operator, $\Omega$ is a probability space and $X$ is a complete metric space. The inverse problem is solved by recourse to the collage theorem for contractive maps. We then consider two applications: (i) random integral equations and (ii) random iterated function systems with greyscale maps (RIFSM), for which noise is added to the classical IFSM.

**Keywords:** Random fixed point equations; collage theorem (search for similar items in EconPapers)

**Date:** 2006-06-23

**Note:** oai:cdlib1:unimi-1030

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