Abstract
We introduce the cluster index of a multivariate stationary sequence and
characterize the index in terms of the spectral tail process. This index plays a major
role in limit theory for partial sums of sequences. We illustrate the use of the cluster
index by characterizing infinite variance stable limit distributions and precise large
deviation results for sums of multivariate functions acting on a stationary Markov
chain under a drift condition.
characterize the index in terms of the spectral tail process. This index plays a major
role in limit theory for partial sums of sequences. We illustrate the use of the cluster
index by characterizing infinite variance stable limit distributions and precise large
deviation results for sums of multivariate functions acting on a stationary Markov
chain under a drift condition.
| Original language | English |
|---|---|
| Journal | Probability Theory and Related Fields |
| Volume | 159 |
| Pages (from-to) | 157-196 |
| ISSN | 0178-8051 |
| DOIs | |
| Publication status | Published - Jun 2014 |