Two Ergodic Sample-Path Properties of the Poisson Process

Wolfgang Stadje
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Wolfgang Stadje: Universität Osnabrück, FB 6

Journal of Theoretical Probability, 1998, vol. 11, issue 1, 197-208

Abstract: 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.

Keywords: Poisson process; ergodic theorem (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021603210282

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