Limit theorems for increments of compound renewal processes

We derive universal strong limit theorems for increments of compound renewal processes which unifies the strong law of large numbers, the Erdős–Rényi law, the Csörgő-Révész law and the law of the iterated logarithm for such processes. New results are obtained under various moment assumptions on distributions of random variables generating the process. In particular, it is investigated the case of distributions from domains of attraction of a normal law and completely asymmetric stable laws with index $\alpha\in(1,2)$.