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Partial sum processes and continued fractions

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  • Athreya, Jayadev S.
  • Athreya, Krishna B.

Abstract

Given{Xi}i=1∞, a sequence of real valued random variables, we define S0=0, Sn=∑i=1nXi, and define the normalized partial sum process{Yn(t):0≤t≤1} by linear interpolation of Ynin=SiSn (assuming P(Sn=0)=0 for all n≥1). In this note the convergence of Yn(⋅) in [0,1] is investigated under various assumptions on {Xi}i=1∞. Of particular interest is the special case where the Xi are the coefficients in the continued fraction expansion of a point x∈[0,1] chosen according to Gauss measure.

Suggested Citation

  • Athreya, Jayadev S. & Athreya, Krishna B., 2017. "Partial sum processes and continued fractions," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 57-62.
    • Handle: RePEc:eee:stapro:v:130:y:2017:i:c:p:57-62
    DOI: 10.1016/j.spl.2017.07.010
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