On martingale approximation of adapted processes
Probability
2011-09-13 v1
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 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.
Keywords
Cite
@article{arxiv.1109.2319,
title = {On martingale approximation of adapted processes},
author = {Hervé Queffélec and Dalibor Volný},
journal= {arXiv preprint arXiv:1109.2319},
year = {2011}
}
Comments
A version of a paper accepted to JOTP (2011)