Opmerkingen en berekeningen betreffende "Poisson-proces met interrupties" van J. C. A. Zaat

Summary
In an earlier paper by J.C. A. ZAAT an interrupted Poisson process was studied. Here we clarify some of the results there obtained. The process is obtained from a stationary Poisson process on the real axis by covering the axis with a sequence of adjoining intervals which have alternatively length a and b, the first left-hand endpoint of an a-interval to the right of 0 being chosen in a stochastic point with has a rectangular distribution over b, a + b]. The interrupted process is periodic and non-stationary. The common distribution function of the interval lengths in the interrupted process is denoted by G(y). Its Laplace-Stieltjes transform is obtained.
If has a rectangular distribution on 0, a + b] the interrupted Poisson process is stationary, but the distribution of the length of an interval between two successive points in the interrupted process is now different for different intervals. For each distribution ofy over 0, a + b] the distribution of the length of the interval between the nth and the (n + I)st point to the right ofO in the interrupted Poisson process tends to the distribution function G(y) as n tends to infinity. Somehow ZAAT based his calculations exclusively on this stationary distribution.