### Laplace Functional Approach to Point Processes Occurring in a Traffic Model

P. Zeephongsekul
Source: Ann. Probab. Volume 9, Number 6 (1981), 1034-1040.

#### Abstract

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.

First Page:
Primary Subjects: 60E05
Secondary Subjects: 60K30, 60B10
Full-text: Open access