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  • 1 Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden
  • 2 Department of Number Theory and Probability Theory, Ulm University, D-89069 Ulm, Germany
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Abstract  

A paper by Chow [3] contains (i.a.) a strong law for delayed sums, such that the length of the edge of the nth window equals n α for 0 < α < 1. In this paper we consider the kind of intermediate case when edges grow like n=L(n), where L is slowly varying at infinity, thus at a higher rate than any power less than one, but not quite at a linear rate. The typical example one should have in mind is L(n) = log n. The main focus of the present paper is on random field versions of such strong laws.