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Iterates of expanding maps
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  • Published: February 2000

Iterates of expanding maps

  • A. D. Barbour1,
  • R. M. Gerrard2 &
  • G. Reinert3 

Probability Theory and Related Fields volume 116, pages 151–180 (2000)Cite this article

  • 94 Accesses

  • 12 Citations

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Abstract.

The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random. In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling and Stein's method.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurer Str. 190, CH-8057 Zürich, Switzerland. e-mail: adb@amath.unizh.ch, , , , , , CH

    A. D. Barbour

  2. The City University, Northampton Square, London EC1V 0HB, USA, , , , , , US

    R. M. Gerrard

  3. Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA, , , , , , US

    G. Reinert

Authors
  1. A. D. Barbour
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  2. R. M. Gerrard
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  3. G. Reinert
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Additional information

Received: 27 June 1997 / Revised version: 21 September 1998

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Cite this article

Barbour, A., Gerrard, R. & Reinert, G. Iterates of expanding maps. Probab Theory Relat Fields 116, 151–180 (2000). https://doi.org/10.1007/PL00008725

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  • Issue Date: February 2000

  • DOI: https://doi.org/10.1007/PL00008725

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  • Mathematics Subject Classification (1991): 58F08, 58F11, 60F05, 60F17, 60G10
  • Key words: Expanding maps – Functional iteration – Coupling – Decay of correlations – Gaussian approximation
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