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December, 1981 Laplace Functional Approach to Point Processes Occurring in a Traffic Model
P. Zeephongsekul
Ann. Probab. 9(6): 1034-1040 (December, 1981). DOI: 10.1214/aop/1176994274


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.


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P. Zeephongsekul. "Laplace Functional Approach to Point Processes Occurring in a Traffic Model." Ann. Probab. 9 (6) 1034 - 1040, December, 1981.


Published: December, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0483.60042
MathSciNet: MR632976
Digital Object Identifier: 10.1214/aop/1176994274

Primary: 60E05
Secondary: 60B10 , 60K30

Keywords: $z$-processes , doubly stochastic Poisson processes , Laplace functional , weak convergence

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 6 • December, 1981
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