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Random Logistic Maps II. The Critical Case

Author

Listed:
  • K. B. Athreya

    (Cornell University)

  • H.-J. Schuh

    (Johannes Gutenberg-Universität)

Abstract

Let (X n )∞ 0 be a Markov chain with state space S=[0,1] generated by the iteration of i.i.d. random logistic maps, i.e., X n+1=C n+1 X n (1−X n ),n≥0, where (C n )∞ 1 are i.i.d. random variables with values in [0, 4] and independent of X 0. In the critical case, i.e., when E(log C 1)=0, Athreya and Dai(2) have shown that X n → P 0. In this paper it is shown that if P(C 1=1)

Suggested Citation

  • K. B. Athreya & H.-J. Schuh, 2003. "Random Logistic Maps II. The Critical Case," Journal of Theoretical Probability, Springer, vol. 16(4), pages 813-830, October.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:4:d:10.1023_b:jotp.0000011994.90898.81
    DOI: 10.1023/B:JOTP.0000011994.90898.81
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    References listed on IDEAS

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    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.
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