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Ergodic path properties of processes with stationary increments
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 2002