Scheffler, Hans-Peter; Becker-Kern, Peter A law of the iterated logarithm for randomly stopped sums of heavy tailed random vectors. (English) Zbl 0964.60034 Monatsh. Math. 130, No. 4, 329-347 (2000). Authors’ abstract: Let \(X_1\), \(X_2\), be an i.i.d. sequence of \(\mathbb{R}^d\)-valued random vectors belonging to the generalized domain of semistable attraction of some nonnormal law. Assume further that \((T_n)\) is a sequence of positive integer valued random variables such that for some \(\delta_0> 0\) \[ (\log n)^{\delta_0} \Biggl|{T_n\over n}- D\Biggr|\to 0\quad\text{a.s.} \] for some discrete positive random variable \(D\), where we do not assume that \((X_n)\) and \((T_n)\) are independent. Let \(S_n= \sum^n_{i=1} X_i\). Then various laws of the iterated logarithm for the norm of \((S_{T_n})\) as well as the radial projection \(\langle S_{T_n},\theta\rangle\) onto a unit vector \(\theta\) are presented. Reviewer: Allan Gut (Uppsala) Cited in 5 Documents MSC: 60F15 Strong limit theorems 60E07 Infinitely divisible distributions; stable distributions 60F05 Central limit and other weak theorems Keywords:regularly varying measures; generalized domains of semistable attraction; operator semistable laws; randomly stopped sums; law of the iterated logarithm PDFBibTeX XMLCite \textit{H.-P. Scheffler} and \textit{P. Becker-Kern}, Monatsh. Math. 130, No. 4, 329--347 (2000; Zbl 0964.60034) Full Text: DOI