ON SOME PROPERTIES OF POISSON PROCESSES

The Poisson process,i.e.,the simple stream,is defined by Khintchine as a stationary,orderlyand finite stream without after-effects.A necessary and sufficient condition for a stream to be asimple stream is that the interarrival times are independent random variables with identicalexponential distributions.This paper gives a simple and rigorous proof of the necessary and sufficientcondition,and discusses the other necessary and sufficient conditions for a renewal process to be aPoisson process.