On multivariate records from random vectors with independent components

@article{Falk2018OnMR,
  title={On multivariate records from random vectors with independent components},
  author={Michael Falk and Amir Khorrami Chokami and Simone A. Padoan},
  journal={Journal of Applied Probability},
  year={2018},
  volume={55},
  pages={43 - 53}
}
Abstract Let X1, X2, . . . be independent copies of a random vector X with values in ℝd and a continuous distribution function. The random vector Xn is a complete record, if each of its components is a record. As we require X to have independent components, crucial results for univariate records clearly carry over. But there are substantial differences as well. While there are infinitely many records in the d = 1 case, they occur only finitely many times in the series if d ≥ 2. Consequently… 
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