A filtered ASTA property
Recently, a considerable number of papers appeared where the PASTA (Poisson Arrivals See Time Averages) property, a notion coined by \textit{R. W. Wolff} [Oper. Res. 30, 223-231 (1982; Zbl 0489.60096)], has been extended to a more general framework. In particular, it has been shown that Poissonianity of a point process embedded in a continuous-time process is not necessary for the coincidence of embedded and non-embedded stationary distributions of the continuous-time process. The assumption that certain conditional intensities of the embedded point process are equal to its (unconditional) intensity turns out to be sufficient and necessary for the coincidence property mentioned. In the present paper, conditions are found which ensure that from the coincidence of embedded and non-embedded stationary distributions of the continuous-time process it follows that not only conditional and unconditional intensities are equal, but that, moreover, a certain conditional embedded point process as a whole is a probabilistic replica of the original (unconditional) one. Examples are given (e.g. Cox processes) for which these conditions are satisfied. A discrete-time version of these results has been obtained as well.
coincidence of embedded and non-embedded stationary distributions
sufficient and necessary for the coincidence property
scientific article; zbMATH DE number 98547
scientific article