A. Logachov ; O. Logachova ; A. Yambartsev
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Moderate, large and super large deviations principles for Poisson
process with uniform catastrophes
cm:14900 -
Communications in Mathematics,
April 10, 2025,
Volume 33 (2025), Issue 1
-
https://doi.org/10.46298/cm.14900Moderate, large and super large deviations principles for Poisson
process with uniform catastrophesArticle
Authors: A. Logachov ; O. Logachova ; A. Yambartsev
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A. Logachov;O. Logachova;A. Yambartsev
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.
Comment: 20 pages
Volume: Volume 33 (2025), Issue 1
Published on: April 10, 2025
Accepted on: March 10, 2025
Submitted on: December 5, 2024
Keywords: Mathematics - Probability, 60F10, 60J27