On Martingale Approximation of Adapted Processes |
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| Authors: | Hervé Queffélec Dalibor Volny |
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| Institution: | 1. Laboratoire Paul Painlev?? U.M.R. CNRS 8524, Universit?? Lille-Nord de France USTL, 59655, Villeneuve D??ascq Cedex, France
2. Laboratoire de Math??matiques Rapha?l Salem UMR 6085 CNRS, Universit?? de Rouen, Avenue de l??Universit??, BP.12 Technop?le du Madrillet, 76801, Saint-??tienne-du-Rouvray, France
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| Abstract: | 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 which 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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