Laplace Functional Approach to Point Processes Occurring in a Traffic Model
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.
Permanent link to this document: http://projecteuclid.org/euclid.aop/1176994274
Digital Object Identifier: doi:10.1214/aop/1176994274
Mathematical Reviews number (MathSciNet): MR632976
Zentralblatt MATH identifier: 0483.60042