The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time, a randomly selected portion of the population is eliminated. For this population process, we derive an asymptotic upper bound for the maximum value and prove the local large deviation principle.
This work is supported by FAPESP grant 2017/20482-0.
AL supported by RSF project 18-11-00129. AL thanks the Institute of Mathematics and Statistics of University of São Paulo for hospitality. AY also thanks CNPq and FAPESP for the financial support via the grants 301050/2016-3 and 2017/10555-0, respectively.
"The local principle of large deviations for compound Poisson process with catastrophes." Braz. J. Probab. Stat. 35 (2) 205 - 223, May 2021. https://doi.org/10.1214/20-BJPS472