Solution
= Solution
For independent identically distributed positive <holding times> $S_i$, define $T_0=0$, $T_n=\sum_{i=1}^nS_i$ and the renewal count $X_t=\max\{n:T_n\le t\}$. With $0<\mu=ES_1<\infty$, the renewal strong law is $X_t/t\to1/\mu$ <almost surely>. The <elementary renewal theorem> is $m(t)/t\to1/\mu$, where $m(t)=EX_t$. More generally the rate is zero when the mean <holding time> is infinite, under the usual nonexplosion assumptions.