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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 8, Fasc. ,
pages 133 - 141
 

LAW OF THE ITERATED LOGARITHM - CLUSTER POINTS OF DETERMINISTIC AND RANDOM SUBSEQUENCES

Ingrid Torrang

Abstract: Let oo (Xk)k=1 be a sequence of i.i.d. random variables with mean 0 and finite, positive variance 2 s and let

sum n Sn = Xk, n > 1. k=1
Further, let
* sum oo -e2/2 e ((nk)) = inf(e > 0; (lognk) < oo ), k=3
where (nk) oo k=1 is a strictly increasing subsequence of the positive integers. Then the set of cluster points of V~ ---------- (Snk/ nk log lognk) oo k=3 equals V~ - V~ [-s 2,s 2] a.s. if lim infnk/nk+1 > 0, k-->o o and [- se*((nk)),se*((nk))] a.s. if lim supnk/nk+1 < 1. k-->o o These results are then applied to randomly indexed partial sums.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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