Mathematics – Probability
Scientific paper
2011-09-11
Mathematics
Probability
A version of a paper accepted to JOTP (2011)
Scientific paper
We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration, but no approximation with respect to a larger filtration with respect to wich it is adapted and regular. There exists a stationary process adapted, regular, and having a martingale approximation with respect to a given filtration but not (regular and having a martingale approximation) with respect to the natural filtration.
Queffélec Hervé
Volný Dalibor
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