Partial sum processes and continued fractions

Jayadev S. Athreya and Krishna B. Athreya

Statistics & Probability Letters, 2017, vol. 130, issue C, 57-62

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.

Keywords: Partial Sum Processes; Continued Fractions; Gauss Measure (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.07.010

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