NDLI: Random Logistic Maps. I

Content Provider	Springer Nature Link
Author	Athreya, K. B. Dai, Jack
Copyright Year	2000
Abstract	Let {C $_{i}$}$^{∞}$ $_{0}$ be a sequence of independent and identically distributed random variables with vales in [0, 4]. Let {X $_{n}$}$^{∞}$ $_{0}$ be a sequence of random variables with values in [0, 1] defined recursively by X $_{ n+1}$=C $_{ n+1}$ X $_{n}$(1−X $_{n}$). It is shown here that: (i) E ln C $_{1}$<0⇒X $_{n}$→0 w.p.1. (ii) E ln C $_{1}$=0⇒X $_{n}$→0 in probability (iii) E ln C $_{1}$>0, E \|ln(4−C $_{1}$)\|<∞⇒There exists a probability measure π such that π(0, 1)=1 and π is invariant for {X $_{n}$}. (iv) If there exits an invariant probability measure π such that π{0}=0, then E ln C $_{1}$>0 and −∫ ln(1−x) π(dx)=E ln C $_{1}$. (v) E ln C $_{1}$>0, E \|ln(4−C $_{1}$)\|<∞ and {X $_{n}$} is Harris irreducible implies that the probability distribution of X $_{n}$ converges in the Cesaro sense to a unique probability distribution on (0, 1) for all X $_{0}$≠0.
Starting Page	595
Ending Page	608
Page Count	14
File Format	PDF
ISSN	08949840
Journal	Journal of Theoretical Probability
Volume Number	13
Issue Number	2
e-ISSN	15729230
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2000-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Probability Theory and Stochastic Processes Statistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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