Ergodic properties of Poisson processes with almost periodic intensity

Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A^* and the Palm version A⁰ corresponding to A^*. Let (T_i,i) be the inter-point distance sequence in A and (T_i⁰,i) in A⁰. We prove that forj, the sequence (T_i+j,i) converges in distribution to (T_i⁰,i). If the intensity function is periodic then the convergence is in variation.