Ergodic path properties of processes with stationary increments

Offer Kella, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


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 Lévy process has a version that possesses this ergodic path property.

Original languageAmerican English
Pages (from-to)199-208
Number of pages10
JournalJournal of the Australian Mathematical Society
Issue number2
StatePublished - 2002


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