On Martingale Approximation of Adapted Processes

Hervé Queffélec () and Dalibor Volný ()
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Hervé Queffélec: Université Lille-Nord de France USTL
Dalibor Volný: Université de Rouen

Journal of Theoretical Probability, 2012, vol. 25, issue 2, 438-449

Abstract: 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.

Keywords: Martingale approximation; Filtration; Stationary process; Blaschke product; 60G10; 60G42; 30J10 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0386-z

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