Geodesic
Limit theorems for maxima of sums and renewal processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 261-274

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Let $~\{X_i\}_{i=1,2,\dots}~$ be a sequence of  i.i.d. random variables, $S_n=X_1+\dots+X_n$, and $S_n\to+\infty$ a.s. We discuss necessary and sufficient conditions for the Kolmogorov and Marcinkiewicz–Zygmund type strong laws of large numbers and for the law of the iterated logarithm for renewal processes defined in two different ways. 
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     author = {A. N. Frolov and A. I. Martikainen and J. Steinebach},
     title = {Limit theorems for maxima of sums and renewal processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {261--274},
     publisher = {mathdoc},
     volume = {278},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a15/}
}
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A. N. Frolov; A. I. Martikainen; J. Steinebach. Limit theorems for maxima of sums and renewal processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 261-274. http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a15/