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Two Ergodic Sample-Path Properties of the Poisson Process

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  • Wolfgang Stadje

    (Universität Osnabrück, FB 6)

Abstract

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.

Suggested Citation

  • Wolfgang Stadje, 1998. "Two Ergodic Sample-Path Properties of the Poisson Process," Journal of Theoretical Probability, Springer, vol. 11(1), pages 197-208, January.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:1:d:10.1023_a:1021603210282
    DOI: 10.1023/A:1021603210282
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    Keywords

    Poisson process; ergodic theorem;

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