On the weak convergence of stochastic processes with embedded point processes

The authors consider a stochastic process in continuous time and two point processes on the real line, all jointly stationary. They show that under a certain mixing condition the values of the process at the points of the second point process converge weakly under the Palm distribution with respect to the first point process, and the authors identify the limit. This result is a supplement to two other known results which are mentioned below.