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
Journal: JOURNAL OF THEORETICAL PROBABILITY
Volumen: 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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