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Journal of Theoretical Probability

, Volume 27, Issue 4, pp 1316–1328 | Cite as

Singularity Results for Functional Equations Driven by Linear Fractional Transformations

  • Kazuki Okamura
Article

Abstract

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham’s functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.

Keywords

De Rham’s functional equations Singular measures  Stationary measures 

Mathematics Subject Classification (2010)

60G30 28A78 28A80 

Notes

Acknowledgments

The author wishes to express his gratitude to his adviser Professor Shigeo Kusuoka for his encouragement, and to the referee for his or her comments.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoMeguro-kuJapan

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