2012 / December Volume 7 No.4
Relaxed Sector Condition
| Published Date |
2012 / December
|
|---|---|
| Title | Relaxed Sector Condition |
| Author | |
| Keyword | |
| Download | |
| Pagination | 463-476 |
| 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.
|
| AMS Subject Classification |
60F05, 60J55
|
| Received |
2012-07-14
|
| Accepted |
2012-07-15
|