Abstract
We are concerned with the approximation of probability measures on a compact metric space (X, d) by invariant measures of Iterated Function Systems with Place-Dependent Probabilities (IFSPDP). Using the Collage Theorem, we formulate the corresponding inverse problem and look for an IFSPDPs which map a target measure \(\nu \) as close as possible to itself in terms of an appropriate metric on \({\mathscr {M}}(X)\), the space of probability measures on X.
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Acknowledgements
This research was partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of Discovery Grants (FM and ERV). Support from the Department of Applied Mathematics and the Faculty of Mathematics, University of Waterloo, in the form of research and teaching assistantships (EAM), is also gratefully acknowledged.
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La Torre, D., Maki, E.A., Mendivil, F., Vrscay, E.R. (2018). Inverse Problems Using Iterated Function Systems with Place-Dependent Probabilities. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_11
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DOI: https://doi.org/10.1007/978-3-319-99719-3_11
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