English

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)

R2 v1 2026-06-21T19:03:10.748Z