On martingale approximation of adapted processes

Details On martingale approximation of adapted processes On martingale approximation of adapted processes

2011-09-11

arxiv.org/abs/1109.2319v1

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.

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