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Strong Gaussian approximation for cumulative processes

Probability 2020-06-18 v1

Abstract

We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Koml\'{o}s-Major-Tusn\'{a}dy type are obtained. Provided examples include applications to stopped sums and birth and death processes.

Keywords

Cite

@article{arxiv.2006.09583,
  title  = {Strong Gaussian approximation for cumulative processes},
  author = {Elena Bashtova and Alexey Shashkin},
  journal= {arXiv preprint arXiv:2006.09583},
  year   = {2020}
}
R2 v1 2026-06-23T16:23:31.744Z