Partial sum processes and continued fractions

Athreya, Jayadev S. ; Athreya, Krishna B. (2017) Partial sum processes and continued fractions Statistics & Probability Letters, 130 . pp. 57-62. ISSN 01677152

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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 Yn[Formula presented]=[Formula presented] (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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier B.V.
Keywords:Partial Sum Processes, Continued Fractions, Gauss Measure
ID Code:131549
Deposited On:07 Dec 2022 05:31
Last Modified:07 Dec 2022 05:31

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