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A result regarding convergence of random logistic maps

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  • Dai, Jack Jie

Abstract

Let {Ci}[infinity]0 be i.i.d. random variables with values in [1,4]. Define random variables {Xn}[infinity]0 with values in [0,1] by Xn+1=CnXn(1-Xn). Then under some mild conditions, the probability distribution of Xn converges in variation norm.

Suggested Citation

  • Dai, Jack Jie, 2000. "A result regarding convergence of random logistic maps," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 11-14, March.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:1:p:11-14
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    Citations

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    Cited by:

    1. Niclas Carlsson, 2002. "A Contractivity Condition for Iterated Function Systems," Journal of Theoretical Probability, Springer, vol. 15(3), pages 613-630, July.
    2. Alsmeyer, Gerold, 2016. "On the stationary tail index of iterated random Lipschitz functions," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 209-233.
    3. 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.
    4. Benaïm, Michel & Schreiber, Sebastian J., 2009. "Persistence of structured populations in random environments," Theoretical Population Biology, Elsevier, vol. 76(1), pages 19-34.

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