Two ergodic sample-path properties of the Poisson process
Autor(en): | Stadje, W | Stichwörter: | ergodic theorem; Mathematics; Poisson process; Statistics & Probability | Erscheinungsdatum: | 1998 | Herausgeber: | PLENUM PUBL CORP | Enthalten in: | JOURNAL OF THEORETICAL PROBABILITY | Band: | 11 | Ausgabe: | 1 | Startseite: | 197 | Seitenende: | 208 | Zusammenfassung: | 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 wit discuss the connection to equidistribution notions. |
ISSN: | 08949840 | DOI: | 10.1023/A:1021603210282 |
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