Renewal counting law of large numbers
= Renewal counting law of large numbers
If $0<\mathbb E\xi_1=1/\lambda<\infty$, then the strong law $S_n/n\to1/\lambda$ and the inequalities $S_{N_t}\leq t<S_{N_t+1}$ imply $N_t/t\to\lambda$ almost surely.
= Renewal counting law of large numbers
If $0<\mathbb E\xi_1=1/\lambda<\infty$, then the strong law $S_n/n\to1/\lambda$ and the inequalities $S_{N_t}\leq t<S_{N_t+1}$ imply $N_t/t\to\lambda$ almost surely.