Abstract
For a class of stationary regularly varying and weakly dependent multivariate time series (X n ), we prove the so-called complete convergence result for the space–time point processes of the form \(N_{n} = \sum _{i=1}^{n} \delta _{(i/n, \boldsymbol {X}_{i}/a_{n})}.\) As an application of our main theorem, we give a simple proof of the invariance principle for the corresponding partial maximum process.
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Basrak, B., Tafro, A. A complete convergence theorem for stationary regularly varying multivariate time series. Extremes 19, 549–560 (2016). https://doi.org/10.1007/s10687-016-0253-5
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DOI: https://doi.org/10.1007/s10687-016-0253-5