Local asymptotics for the first intersection of two independent renewals

Kenneth S. Alexander, Quentin Berger

We study the intersection of two independent renewal processes, $\rho =\tau \cap \sigma$. Assuming that $\mathbf{P}({\tau }_1=n)=\phi (n)n^{-(1+\alpha )}$ and $\mathbf{P}(σ_1 = n ) = \tildeφ(n)\, n^{-(1…