Two Ergodic Sample-Path Properties of the Poisson Process |
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Authors: | Wolfgang Stadje |
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Institution: | (1) Universität Osnabrück, FB 6, D-49069 Osnabrück, Germany |
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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. |
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Keywords: | Poisson process ergodic theorem |
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