Limit theorems for maxima of sums and renewal processes

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.