This paper deals with a wide class of point processes which are subsumed under the name of $z$-processes. These processes are generalizations, in the sense that the initial distribution of the vehicles are not necessarily stationary Poisson, of point processes occurring in a traffic model of Renyi (1964). Using the Laplace functional, we derive the distributions of various $z$-processes when the initial process is stationary Poisson and prove a weak convergence result to the doubly stochastic Poisson process when the initial process is not necessarily Poisson distributed.
@article{1176994274,
author = {Zeephongsekul, P.},
title = {Laplace Functional Approach to Point Processes Occurring in a Traffic Model},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 1034-1040},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994274}
}
Zeephongsekul, P. Laplace Functional Approach to Point Processes Occurring in a Traffic Model. Ann. Probab., Tome 9 (1981) no. 6, pp. 1034-1040. http://gdmltest.u-ga.fr/item/1176994274/