Random Logistic Maps II. The Critical Case

K. B. Athreya () and H.-J. Schuh ()
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K. B. Athreya: Cornell University
H.-J. Schuh: Johannes Gutenberg-Universität

Journal of Theoretical Probability, 2003, vol. 16, issue 4, 813-830

Abstract: 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)

Keywords: random logistic maps; critical case; convergence in probability but not w.p.1; empirical distribution (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/B:JOTP.0000011994.90898.81

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