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A Contractivity Condition for Iterated Function Systems

Author

Listed:
  • Niclas Carlsson

    (Åbo Akademi University)

Abstract

We prove a condition for long-term contractivity and the existence of a unique invariant measure for iterated function systems. We also give an intuitive interpretation of the condition in terms of weighted derivatives and weighted Wasserstein metrics. We use our condition in order to show some results for stochastic population models based on the logistic and Ricker maps.

Suggested Citation

  • Niclas Carlsson, 2002. "A Contractivity Condition for Iterated Function Systems," Journal of Theoretical Probability, Springer, vol. 15(3), pages 613-630, July.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:3:d:10.1023_a:1016215831096
    DOI: 10.1023/A:1016215831096
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    References listed on IDEAS

    as
    1. K. B. Athreya & Jack Dai, 2000. "Random Logistic Maps. I," Journal of Theoretical Probability, Springer, vol. 13(2), pages 595-608, April.
    2. Dai, Jack Jie, 2000. "A result regarding convergence of random logistic maps," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 11-14, March.
    Full references (including those not matched with items on IDEAS)

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