On a law of the iterated logarithm for sums mod 1 with application to Benford's law
- Cite this article as:
- Schatte, P. Probab. Th. Rel. Fields (1988) 77: 167. doi:10.1007/BF00334035
- 50 Downloads
Let Zn be the sum mod 1 of n i.i.d.r.v. and let 1[0,x](·) be the indicator function of the interval [0, x]. Then the sequence 1[0,x](Zn) does not converge for any x. But if arithmetic means are applied then under suitable suppositions convergence with probability one is obtained for all x as well-known. In the present paper the rate of this convergence is shown to be of order n-1/2 (loglogn)1/2 by using estimates of the remainder term in the CLT for m-dependent r.v.