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# Random fixed point equations and inverse problems by collage theorem

## Author

Listed:
• Davide La Torre

(University of Milan)

• Herb Kunze
• Edward Vrscay

## 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.

## Suggested Citation

• Davide La Torre & Herb Kunze & Edward Vrscay, 2006. "Random fixed point equations and inverse problems by collage theorem," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1030, Universitá degli Studi di Milano.
• Handle: RePEc:bep:unimip:unimi-1030
Note: oai:cdlib1:unimi-1030
as

File URL: http://services.bepress.com/unimi/statistics/art11

## Citations

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Cited by:

1. 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.
2. Vincenzo CAPASSO & Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "Parameter identification for deterministic and stochastic differential equations using the "collage method" for fixed point equations," Departmental Working Papers 2008-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

### Keywords

Random fixed point equations; collage theorem;

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