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.
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}
}