| Abstract: | The Poisson process, i.e., the simple stream, is defined by Khintchine as a stationary, orderly and finite stream without after-effects. A necessary and sufficient condition for a stream to be a simple stream is that the interarrival times are independent random variables with identical exponential distributions. This paper gives a simple and rigorous proof of the necessary and sufficient condition, and discusses the other necessary and sufficient conditions for a renewal process to be a Poisson process.Institute of Applied Mathematics, Academia Sinica |
