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A note on the characteristics of Poisson processes

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Abstract

In this note two characteristic theorems of Poisson processes are given. If {N(t);t≧0} is a renewal process,U t ,V t are, respectively, the time since the last renewal and the time to the next renewal att, Z t =U t +V t , then a Poisson process can be characterized by the limiting independene of the joint distribution of (U t ,V t ) whent→∞, orEZ t , or the distribution ofZ t .

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References

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    Chung, K. L., The Poisson Process a a Renewal Process.Periodica Mathematica Humgar.,2 (1972), 41–48.

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    Cinlar, E., and Jagers, P., Two Mean Values which Characterize the Poisson Process.J. Appl. Prob.,10 (1973) 678–681.

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    Çinlar, E., and Jagers, P., Introduction to Stochastic Processes. Prentice-Hall Inc., 1975.

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Ying, Y., Kan, C. A note on the characteristics of Poisson processes. Acta Mathematicae Applicatae Sinica 1, 149–152 (1984). https://doi.org/10.1007/BF01669675

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Keywords

  • Poisson Process
  • Joint Distribution
  • Renewal Process
  • Math Application
  • Characteristic Theorem