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

TL;DR

This paper extends the theory of Poisson processes with uniform catastrophes by establishing moderate, large, and superlarge deviation principles across different scalings, providing a comprehensive understanding of their probabilistic behavior.

Contribution

It generalizes previous results by deriving deviation principles for multiple scalings of Poisson processes with catastrophes, introducing new rate functions.

Findings

Established moderate deviation principles for Poisson processes with catastrophes.

Derived large deviation principles with explicit rate functions.

Extended analysis to superlarge deviations, broadening theoretical understanding.

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.