English

Moderate, large and super large deviations principles for Poisson process with uniform catastrophes

Probability 2025-05-29 v3

Abstract

In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear (moderate deviations), linear (large deviations), and superlinear (superlarge deviations). Across these scales, we establish different yet coherent rate functions.

Keywords

Cite

@article{arxiv.2411.19255,
  title  = {Moderate, large and super large deviations principles for Poisson process with uniform catastrophes},
  author = {A. Logachov and O. Logachova and A. Yambartsev},
  journal= {arXiv preprint arXiv:2411.19255},
  year   = {2025}
}

Comments

20 pages

R2 v1 2026-06-28T20:16:05.640Z