J. Austral. Math. Soc.
72 (2002), 199-208
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Ergodic path properties of processes with stationary increments
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Offer Kella
Department of Statistics
The Hebrew University of Jerusalem
Mount Scopus, Jerusalem 91905
Israel
offer.kella@huji.ac.il
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and
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Abstract
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For a real-valued ergodic process X
with strictly stationary increments satisfying
some measurability and continuity assumptions it
is proved that the long-run `average behaviour'
of all its increments over finite intervals
replicates the distribution of the corresponding
increments of X
in a strong sense. Moreover, every Levy
process has a version that possesses this ergodic
path property.
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