J. Austral. Math. Soc.  72 (2002), 199-208
Ergodic path properties of processes with stationary increments

Offer Kella
  Department of Statistics
  The Hebrew University of Jerusalem
  Mount Scopus, Jerusalem 91905
Wolfgang Stadje
  Department of Mathematics
  and Computer Science
  University of Osnabruck
  49069 Osnabruck
  Germany   wolfgang@mathematik.uni-osnabrueck.de

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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