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Relaxed Sector Condition
by Illes Horvath   Balint Toth   Balint Veto

Vol. 7 No. 4 (2012) P.463~P.476

ABSTRACT

In this note we present a new sufficient condition which guarantees martingale approximation and central limit theorem $\textit{a la Kipnis - Varadhan}$ to hold for additive functionals of Markov processes. This condition, which we call the \emph{relaxed sector condition $($RSC$)$} generalizes the strong sector condition (SSC) and the graded sector condition (GSC) in the case when the self-adjoint part of the infinitesimal generator acts diagonally in the grading. The main advantage being that the proof of the GSC in this case is more transparent and less computational than in the original versions. We also hope that the RSC may have direct applications where the earlier sector conditions do not apply. So far we do not have convincing examples in this direction.

KEYWORDS
central limit theorem, additive functionals of Markov processes, sector conditions

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F05, 60J55

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