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A note on iterated function systems with discontinuous probabilities

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  • Jaroszewska, Joanna

Abstract

We consider an example of an iterated function system with discontinuous probabilities. We prove that it posses an invariant probability measure. We also prove that it is asymptotically stable provided probabilities are positive.

Suggested Citation

  • Jaroszewska, Joanna, 2013. "A note on iterated function systems with discontinuous probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 28-31.
    • Handle: RePEc:eee:chsofr:v:49:y:2013:i:c:p:28-31
    DOI: 10.1016/j.chaos.2013.01.012
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    References listed on IDEAS

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    1. Jaroszewska, Joanna, 2013. "On asymptotic equicontinuity of Markov transition functions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 943-951.
    2. Stenflo, Örjan, 2001. "A note on a theorem of Karlin," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 183-187, September.
    3. Ngai, Sze-Man, 2012. "Singularity and L2-dimension of self-similar measures," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 256-265.
    4. Andres, Jan & Fišer, Jiří & Gabor, Grzegorz & Leśniak, Krzysztof, 2005. "Multivalued fractals," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 665-700.
    5. Llorente, Marta & Morán, Manuel, 2012. "An algorithm for computing the centered Hausdorff measures of self-similar sets," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 246-255.
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